Certified Mail Question

I know I can get the answer to this question at my local post office, but I thought I’d ask on here first.
If you send something certified, with return receipt, do you need to put a return address on it?
My wife is the administrator of her mothers estate and needs to send a certified check to her (my wife’s) brother. We want nothing to do with him, nor do we want him to know where we live. We just need to fulfill the obligation.
He disappeared when his mother was dying last September. He has resurfaced in text messages. He smells money.
If this hasn't already been sent, this is what I suggest.
Send the check registered mail with a return receipt.
If you're not going to add a return address, I suggest this method. This does a couple of things,
1. Anyone within the USPS that touches that letter must sign for it and becomes accountable for it. Registered letters don't get lost. They get special treatment from point A to B.
2. The return receipt will come back to you with a signature.
This service does cost extra.
When I was a mail carrier, not having a return address with a certified letter was always a risky thing. If he doesn't claim the check, (this happens a lot with folks of questionable repute) how will the Post Office return it to you. We didn't (at the P/O level) disturb the return receipt. So if a certified letter goes unclaimed, without a return address, it went to the dead letter office. They may or may not return it to you, if they do, it may take months if not years.
I'm also going to throw this out there, if your BIL really wants to find you, its way to easy. I recently found a family member who hadn't been seen or heard from since 1979. I wrote him to let him know another family member had passed. He, surprisingly, attended the visitation and we spoke briefly. His #2 question was how I found him and the answer was Google.
Regardless, good luck.