They will check your documents at SJU. Just be sure to check in at the gate. When we flew we had checked bags so it was more complicated as we had to pick up our checked luggage, transit to the ticket counters, check in with silver, then through security again, then back to the pit of despair (gate D). Folks who skipped that process and went gate to gate because they only had carry on luggage still needed to check in at the gate… Silver checked documents for the correct markings indicating that you had presented your documents. Some people neglected to check in at the gate thinking their boarding passes were enough but they were held up until they showed their documents.