This is a mortgage underwriting question at its core, and the accurate answer requires a licensed mortgage professional, specifically a loan officer who works with FHA and conventional files regularly. I can explain the general mechanics so you know what to ask them, but please treat what follows as a starting point for that conversation, not a substitute for it.
Here is how the pieces generally work.
The option fee is not a gift, not earnest money, and not interchangeable with a purchase credit. Each of those terms has a specific meaning in an underwriting file. Lenders care about the source of every dollar that touches a transaction because they are trying to confirm the buyer is not secretly borrowing the down payment.
When a tenant-buyer exercises the option, the question becomes whether the option fee can be counted toward the down payment or closing costs. Conventional guidelines (Fannie Mae and Freddie Mac) generally allow rent credits and option fees to reduce the required cash to close, but only if they are documented in writing from the start and do not exceed the market rent differential or the actual amount paid. FHA has its own rules, and they differ in the details. Both programs will want to see the original lease-option agreement as the source document.
Your sandwich question is the sharper one. If the option fee went to an investor in the middle rather than to the actual property owner, that creates a sourcing and disclosure problem. The lender will want to trace where that money went and whether it reduces the seller's net proceeds. That structure needs careful legal and financial documentation, and I would confirm it with both a real estate attorney and a mortgage professional before building a deal around it.
One thing worth knowing: the Rena strategy guide for lease options specifically flags legal precision and documentation as the biggest practical challenge. That note about keeping the option contract separate from the lease is directly relevant here.
What loan type is your current escrow using? That context would help a loan officer give you a more targeted answer when you ask them.