There are many guides of how to configure FBA in Sharepoint 2013 (e.g. here). One of the common problem with FBA in Sharepoint is that People picker doesn’t resolve FBA user names. How to fix this issue? Let’s use assumption that you followed configuration guide mentioned above and did all steps described there.
One of the most common solutions for this problem is that you need to add necessary permissions for identity of application pool of your web application to FBA database:
If you did it and it didn’t help try to search FBA user by full claims login name. E.g. suppose that we have user “superuser” in FBA database. Then claims login name will be “i:0#.f|fba_membership|superuser” (fba_membership is the name of membership provider configured in web.config of your web application, central administration and secure token service). It should find the user and after that People picker should successfully resolve FBA users.