there may be two ways of doing this:

1) using Table Valued Parameters

2) By passing the filter that will be used to determine the result set from TableA and perform an innser join using that, e.g.

CREATE PROCEDURE MyProcedure

@p_name1 DataType, @p_name2 DataType

FROM TableB

INNER JOIN Table A ON TableA.Column = TableB.Column AND TableA.OtherColumn = @p_name1

WHERE TableB.AnotherColumn = @p_name2