the complete activity report shows the last access time in the place the first time access should be.
(e.g. course/user.php?id=3&user=2&mode=complete )

I've resiolved it on my own this way:

in the function below I've added the lines commented as josef:

mod/scorm/locallib.php


function scorm_get_tracks($scoid,$userid,$attempt='') {
/// Gets all tracks of specified sco and user
    global $CFG;

    if (empty($attempt)) {
        if ($scormid = get_field('scorm_scoes','scorm','id',$scoid)) {
            $attempt = scorm_get_last_attempt($scormid,$userid);
        } else {
            $attempt = 1;
        }
    }
    $attemptsql = ' AND attempt=' . $attempt;
    if ($tracks = get_records_select('scorm_scoes_track',"userid=$userid AND scoid=$scoid".$attemptsql,'element ASC')) {
        $usertrack->userid = $userid;
        $usertrack->scoid = $scoid;
        // Defined in order to unify scorm1.2 and scorm2004
        $usertrack->score_raw = '';
        $usertrack->status = '';
        $usertrack->total_time = '00:00:00';
        $usertrack->session_time = '00:00:00';
        $usertrack->timemodified = 0;
        $usertrack->firsttimemodified = time(); // josef
        foreach ($tracks as $track) {
            $element = $track->element;
            $usertrack->{$element} = $track->value;
            switch ($element) {
                case 'cmi.core.lesson_status':
                case 'cmi.completion_status':
                    if ($track->value == 'not attempted') {
                        $track->value = 'notattempted';
                    }
                    $usertrack->status = $track->value;
                break;
                case 'cmi.core.score.raw':
                case 'cmi.score.raw':
                    $usertrack->score_raw = $track->value;
                break;
                case 'cmi.core.session_time':
                case 'cmi.session_time':
                    $usertrack->session_time = $track->value;
                break;
                case 'cmi.core.total_time':
                case 'cmi.total_time':
                    $usertrack->total_time = $track->value;
                break;
            }
            if (isset($track->timemodified) && ($track->timemodified > $usertrack->timemodified)) {
                $usertrack->timemodified = $track->timemodified;
            }
            if (isset($track->timemodified) && ($track->timemodified < $usertrack->firsttimemodified)) { // josef
                $usertrack->firsttimemodified = $track->timemodified; // josef
            } // josef
        }
        if (is_array($usertrack)) {
            ksort($usertrack);
        }
        return $usertrack;
    } else {
        return false;
    }
}




mod/scorm/lib.php

function scorm_user_complete($course, $user, $mod, $scorm) {
    global $CFG;

    $liststyle = 'structlist';
    $scormpixdir = $CFG->modpixpath.'/scorm/pix';
    $now = time();
    $firstmodify = $now;
    $lastmodify = 0;
    $sometoreport = false;
    $report = '';
    
    if ($orgs = get_records_select('scorm_scoes',"scorm='$scorm->id' AND organization='' AND launch=''",'id','id,identifier,title')) {
        if (count($orgs) <= 1) {
            unset($orgs);
            $orgs[]->identifier = '';
        }
        $report .= '<div class="mod-scorm">'."\n";
        foreach ($orgs as $org) {
            $organizationsql = '';
            $currentorg = '';
            if (!empty($org->identifier)) {
                $report .= '<div class="orgtitle">'.$org->title.'</div>';
                $currentorg = $org->identifier;
                $organizationsql = "AND organization='$currentorg'";
            }
            $report .= "<ul id='0' class='$liststyle'>";
            if ($scoes = get_records_select('scorm_scoes',"scorm='$scorm->id' $organizationsql order by id ASC")){
                // drop keys so that we can access array sequentially
                $scoes = array_values($scoes);
                $level=0;
                $sublist=1;
                $parents[$level]='/';
                foreach ($scoes as $pos=>$sco) {
                    if ($parents[$level]!=$sco->parent) {
                        if ($level>0 && $parents[$level-1]==$sco->parent) {
                            $report .= "\t\t</ul></li>\n";
                            $level--;
                        } else {
                            $i = $level;
                            $closelist = '';
                            while (($i > 0) && ($parents[$level] != $sco->parent)) {
                                $closelist .= "\t\t</ul></li>\n";
                                $i--;
                            }
                            if (($i == 0) && ($sco->parent != $currentorg)) {
                                $report .= "\t\t<li><ul id='$sublist' class='$liststyle'>\n";
                                $level++;
                            } else {
                                $report .= $closelist;
                                $level = $i;
                            }
                            $parents[$level]=$sco->parent;
                        }
                    }
                    $report .= "\t\t<li>";
                    if (isset($scoes[$pos+1])) {
                        $nextsco = $scoes[$pos+1];
                    } else {
                        $nextsco = false;
                    }
                    if (($nextsco !== false) && ($sco->parent != $nextsco->parent) && (($level==0) || (($level>0) && ($nextsco->parent == $sco->identifier)))) {
                        $sublist++;
                    } else {
                        $report .= '<img src="'.$scormpixdir.'/spacer.gif" alt="" />';
                    }

                    if ($sco->launch) {
                        require_once('locallib.php');
                        $score = '';
                        $totaltime = '';
                        if ($usertrack=scorm_get_tracks($sco->id,$user->id)) {
                            if ($usertrack->status == '') {
                                $usertrack->status = 'notattempted';
                            }
                            $strstatus = get_string($usertrack->status,'scorm');
                            $report .= "<img src='".$scormpixdir.'/'.$usertrack->status.".gif' alt='$strstatus' title='$strstatus' />";
                            if ($usertrack->timemodified != 0) {
                                if ($usertrack->timemodified > $lastmodify) {
                                    $lastmodify = $usertrack->timemodified;
                                }
                                if ($usertrack->firsttimemodified < $firstmodify) { // josef
                                    $firstmodify = $usertrack->firsttimemodified; // josef
                                }
                            }
                        } else {
                            if ($sco->scormtype == 'sco') {
                                $report .= '<img src="'.$scormpixdir.'/'.'notattempted.gif" alt="'.get_string('notattempted','scorm').'" title="'.get_string('notattempted','scorm').'" />';
                            } else {
                                $report .= '<img src="'.$scormpixdir.'/'.'asset.gif" alt="'.get_string('asset','scorm').'" title="'.get_string('asset','scorm').'" />';
                            }
                        }
                        $report .= "&nbsp;$sco->title $score$totaltime</li>\n";
                        if ($usertrack !== false) {
                            $sometoreport = true;
                            $report .= "\t\t\t<li><ul class='$liststyle'>\n";
                            foreach($usertrack as $element => $value) {
                                if (substr($element,0,3) == 'cmi') {
                                    $report .= '<li>'.$element.' => '.$value.'</li>';
                                }
                            }
                            $report .= "\t\t\t</ul></li>\n";
                        }
                    } else {
                        $report .= "&nbsp;$sco->title</li>\n";
                    }
                }
                for ($i=0;$i<$level;$i++) {
                    $report .= "\t\t</ul></li>\n";
                }
            }
            $report .= "\t</ul><br />\n";
        }
        $report .= "</div>\n";
    }
    if ($sometoreport) {
        if ($firstmodify < $now) {
            $timeago = format_time($now - $firstmodify);
            echo get_string('firstaccess','scorm').': '.userdate($firstmodify).' ('.$timeago.")<br />\n";
        }
        if ($lastmodify > 0) {
            $timeago = format_time($now - $lastmodify);
            echo get_string('lastaccess','scorm').': '.userdate($lastmodify).' ('.$timeago.")<br />\n";
        }
        echo get_string('report','scorm').":<br />\n";
        echo $report;
    } else {
        print_string('noactivity','scorm');
    }

    return true;
}