You do not have to wait. Send it now if you want to, and here is why.
InmateAid has a standing policy that covers exactly this situation. If your inmate gets transferred and a letter, postcard, or any other item gets caught in the move and fails to reach them, InmateAid will resend or replace everything at no charge. No questions, no fees, no hassle.
The only thing you need to do is let them know what happened. Send an email to aid@inmateaid.com with your inmate's new facility information and InmateAid will update the record and get your mail back out the door to the correct location. That is the whole process.
The practical upside to sending now rather than waiting is that if the transfer gets delayed, as prison transfers often do, your letter is already on its way and arrives on schedule. If the transfer goes through before delivery, you are covered. Either way you are not losing anything by moving forward today.
Staying in contact during a transfer is important. Inmates in transit can go days or weeks with limited communication, and knowing a letter is coming means something even before it arrives.