I don't see anything wrong in taking screenshots as long as he isn't doing that with sensitive data such as passwords, seed phrases, phone numbers, private keys, and other important stuff that one can use to access his accounts or funds in case his phone gets lost or stolen or gets in the hands of a person who could do something like that. Taking screenshots of the transactions isn't a bad thing because sometimes you might need in future for a certain transaction you did, this is mostly required when you are doing P2P trades online.

There are a lot of scammers in P2P marketplaces who would initiate trades with you, take your money, and then open disputes and stuff to get their funds back to their account while they have already taken payment from you. In such situations, you need payment screenshots that you can send to the support team to back your case.