twitter is apparently getting rid of faves/likes
and nobody knows what will happen to your faves, so

how to backup your twitter faves

1) open a new tab in chrome or firefox

2) press F12

3) if chrome:   open the "Network" tab
   if firefox:  open the "Network Monitor" tab

4) in that tab, go to https://twitter.com/i/likes

5) hold the END key until you hit the bottom for real
   (you'll see the twitter logo and "Back to top")

6) rightclick any of the entries in the networks list

7) if chrome:   select "Save as HAR with content"
   if firefox:  select "Save All as HAR"

in the event that twitter actually /does/ remove faves,
this document will be updated with a link to a python script
which converts this .har file to an html file containing a
list of the tweets you had faved, so keep it safe