Use of a possessive determiner or "the"

I will sell his collection of books in the same way I did with my collection of paintings and the other one consisting of letters.

As I read that, I have no idea to whom the collection of letters belongs. It could be his, yours, or someone else's.

I will assume that it is yours:

"I will sell his collection of books in the same way I did with my collection of paintings and the other one consisting of my collection of letters."

In reality, as there will be context and so, "I will sell his collection of books in the same way I did my collections of paintings and letters" could work.