Script to accept &uid=whatever and store it into the new donation's uid field.

donation_uid.html

<script type="text/javascript">
    // Add donation.uid to the form and populate it with the contents of the
    // `uid` query in the URL.
    // @see https://salsasupport.zendesk.com/entries/98784548
    $(document).ready(function() {
        if (window.location.href.indexOf('public/?donate_page_KEY=') == -1) {
            return;
        }
        var searches = window.location.search.split('&')
            .reduce(function(a, x) { 
                var parts = x.split('=');
                a[parts[0]] = (parts.length > 1) ? parts.splice(1).join('=') : null;
                return a;
            }, {});
        if (searches.hasOwnProperty('uid')) {
            // @note The UID *must* appear at the end of the form. If it's not there
            // then Salsa will apply it to the supporter record.
            $('form[name=subform]').append(''
                + '<input type="hidden" name="object" value="donation"/>'
                + '<input type="hidden" name="uid" value="' + searches['uid'] + '"/>');
        };
    });
</script>