Assume we have two separate lists of emails handled by two different processors. List A is gathered by company A in a way that the subject has given their consent for its processing for marketing purposes. List B is gathered by company B in a way that the user gives no specific consent for any marketing use.
If company A sends emails to company B, and company B responds with "yes, this exists in our database" or "no, this does not exist in our database" - does that require company B to gather consent from the subject?
I have been unable to find any information relating to this scenario in terms of what GDPR requires. I suspect it requires company B to get consent from its subjects, but I cannot find any specific support for this in GDPR.
EDIT: As people have pointed out in the comments, companies A and B are controllers here and not processors; excuse me for my misuse of the terminology.