I have flown thru SJU to several times recently. I have been on American Airlines and booked with Intercaribbean separately so it may be different. In my case you simply collect your bags at baggage claim and take the elevator there in the baggage claim area upstairs and check in at the I/C counter. Two points, their counter is at the far end of the terminal and it is only maned a couple hours before the next scheduled flight. The TSA line can be long and slow so if you have TSA Precheck it will help a bunch.