The usual provisos about jurisdictional differences may apply, and the last sentence of the first paragraph currently uses "account" to relate to two different things - I'll assume that sentence means "Person B then uses person A's user information to trade the account".
It's clear that XYZ expected the two users of the account to use different user identifications - they issued two. An accusation of misrepresentation is most likely to come from the brokerage firm, though it could also come from an internal or external auditor or from A if A assumed that B knew that they were expected to use their own user identification.
There may be mitigation - if A said to B "Here's authority to use the account : these are my login details", and/or if XYZ did not effectively communicate the separate user details to B, a Reasonable Person could conclude that B had not knowingly misrepresented themselves as A.
As the question stands it looks like an accusation of misrepresentation against B would be both possible and reasonable.