Recommender sent me letter to submit
Edit after some exchange in the comments below: I recommend that you contact the writer of the third letter and tell them that what you really need is them to send the letter directly when asked, and to pass on contact details now. This problem seems to be the result of a misunderstanding, and busy high profile researcher or not, if a misunderstanding is happening, it makes sense to clarify things. If you don't get a response, you can still use the letter you have.
Original answer:
Personally I wouldn't have worried about simply including the letter. What's wrong with that? It's a good letter, and if they don't believe it is genuine they can contact the writer. Where I work, such letters are not that important anyway. Personally I'm fine if a candidate is able to present two or three such letters by qualified people in which there is nothing worrying, and that's it. As most candidates fulfill that, these letters play no further role in decision making (frankly even unsuitable candidates can come up with glowing reference letters, so these are not that informative; even some high profile people write nice letters for everyone). Of course I can't guarantee it's like that everywhere.