License purchase for a client in the name of another client

I have a very specific question that relates to license transfer to clients - I am a freelance designer working for a client (Client 1) who is coordinating marketing material and a website for another client (Client 2). Client 1 has asked me to (1) purchase an extended license for a photo (not an editorial photo) through Adobe Stock, (2) edit the photo, (3) give them the edited photo to be used on a website and a brochure for Client 2 and (4) charge Client 1 for the cost of the license.

As I understand, I can transfer the edited photo to Client 1, as long as I get written consent to follow the terms and to only use this photo as part of this work. What I am not sure is:

- can I charge Client 1 for the license fee?

- can Client 1 send the photo to subcontractors to be used in brochures and a website for Client 2?

- am I doing anything wrong?

This is all very confusing, any help understanding this all would be greatly appreciated...