Hallo João
do I understand you correctly that you changed the screen entry from SAPR3 to SAPSR3?
You are correct that the standard user is SAPSR3. However, you are performing a system copy hence the schema owner depends on you source database as well as your copy procedure.
My understanding is that the schema can only be changed if you perform a system copy using export/import. If you use backup/restore (which is most widely used) you can not change the schema.
Conclusion: Assuming you are using backup/restore to perform your system copy, you shouldn't have adjusted the ABAP schema owner but should have kept SAPR3.
Regards
Thomas.