Save this query as qryIDSub, for example. Of course, ID and Table A in the SQL statement should be substituted with the correct object names.
2) Another query:
DELETE * FROM Table B INNER JOIN qryIDSub ON Table B.ID = qryIDSub.ID
That should work.
The point is, you have to isolate the unique IDs within Table A before you can run the delete query.
BTW, Access will probably not even delete as requested, and may give you an error message "must use updateable query". If that's the case run the first query (qryIDSub) as a make-table query and make a new name, and change the second query (the delete query) to use the new temp table in the INNER JOIN.