It has been contemplated (and codified in the AA Ecosystem Participation Terms) that a citizen must be provided the ability by an AA to “download” his/her consents and conversely, to “upload” consents hitherto managed by a different AA.
The technical details of this are yet to be worked out.
However, while this will help provide choice to citizens in the event they wish to change their consent manager, this is not relevant to the issue of whether a user can set up a profile with one AA and share data with an FIU via another AA.