s2 is pretty much dead in my eyes- even though they keep denying it from time to time - and promise updates - but the last update is well over a year ago by now. Essentially since 2011 except from the Stripe integration nothing ever changed besides bugfixes. So s2 is really old tech (not problematic in some places as it works well there even being complicated, but very problematic for some other things).
However to your question - you will need to have the relevant fields filled out - just do a checkout with paypal for a small amount with subscription - and make sure the old users are having the same fields filled. (
Paid Subscr. Gateway: [?]
Paid Subscr. ID
Custom Value (filled in with your domain name - but maybe also with whatever your old plugin set here at paypal - so this is the critical field where I would not be sure what to set if your old plugin did not use domain name).
HOWEVER - do you really want to switch to S2? Is the support good enough for you? Do you trust them to update s2? Do you trust them to fix s2 for Gutenberg WP 5.0 (right now it causes havoc from my understanding). Optimizepress incorporates s2member labeled as OPM and they provide very good support - still it will mean all s2 shortcomings more or less. If you move why not move to some modern membership plugin?