From aerial imagery it looks like the two car lanes on westbound Avalon must turn left onto Fauntleroy, and the bike lane can either turn right onto Fauntleroy via the link, turn left onto Fauntleroy into a third car lane, or turn left onto 36th via the islands and crosswalks (which are designated for this purpose).

I’ve added a turn restriction with an exception for bicycles. Not sure what the intended use of the link is now so I’ve left its tags unchanged. (In theory a car could back onto it from Fauntleroy?)