I've had pulley issues and i've actually used a fingerboard to rehabilitate successfully
For me on a fingerboard I can completely focus on my grip, on the way my hand holds the edge, and really understand the way the fingers interact with the hold. This lets me train and also rehabilitate the fingers in a safe as possible way, whereas while doing hard bouldering, peak forces and hand positions and loadings are more unpredictable.
What i did is work up from openhanded(dragging), to assisted open crimp("Half crimp"), to unassisted open crimp on the injured hand, backing off at any sign of pain. With the half crimp on the injured hand, work from a more open crimp up progressively into a half crimp, paying attention to pain signals. Half crimp puts more pressure on the a2 pulley whereas open hand does so minimally, so work slowly into it.
Before, between sets and after each session i would do the "squeeze test" where i squeeze the injured area and pay attention to any abnormal signs of pain. (You can use the healthy hands finger or surrounding fingers as a control to see if the pain is abnormal. ) If there is any sign of pain i back off until it gets better.
I also did contrast baths/ice therapy during this period which seemed to help a great deal - as measured anecdotedly by the "squeeze test"
One major benefit of doing this compared to just climibng is that when you are rehabilitated, you will be able to half crimp while climbing with confidence that you aren't going to blow something out.
