Figured it out. If anybody wants to do the same, open up list of favorites in mobile mode. URL for that should be
https://m.fanfiction.net/m/f_story.phpRight-click, then Inspect. Go to console and paste the following code
var x = document.querySelectorAll("a");
var myarray = []
for (var i=0; i<x.length; i++){
var nametext = x[i].textContent;
var cleantext = nametext.replace(/\s+/g, ' ').trim();
var cleanlink = x[i].href;
myarray.push([cleantext,cleanlink]);
};
function make_table() {
var table = '<table><thead><th>Name</th><th>Links</th></thead><tbody>';
for (var i=0; i<myarray.length; i++) {
table += '<tr><td>'+ myarray[i][0] + '</td><td>'+myarray[i][1]+'</td></tr>';
};
var w = window.open("");
w.document.write(table);
}
make_table()
Run it, it will give you table containing all links. Copy-paste to excel, remove every other row (those are links to the author) and you are left with list of all your favorited stories.
To download them just copy-paste it into FFF. I suggest limiting yourself to 100 at a time