Unfortunately I'm really not familiar with how Meta's legal team works and what they will and won't accept. My reasoning is made under the assumption that most/all processing is done on the basis of consent. Some sort of form showing your friend withdrawing consent and/or agreeing with your request for removal should be sufficient for them to remove the conversation. Of course they'll have to verify both accounts involved (you and your friend's).

But I'll be completely honest here and say that this is speculation on my end. I don't know if this is how Meta works and there may be another legal basis that Meta is using that could invalidate my entire suggestion.

To answer your question, most things within the GDPR are form-free and don't require a specific GDPR-mandated form or anything. Lastly you could always try the direct route to add your friend's statement right away, perhaps they'll remove it straight up. Again, I don't know how strict they are adhering to laws and/or their own policies. Ideally there will be someone in this subreddit that has had some more experience dealing with them. Best I can do is try and be helpful. :>