You will need access to the data and access to a SQL db, you can derive the information via a simple SQL query. This example was written for SQL Server in TSQL.
The query will list the Hydrant (Layer A) and Fire District (Layer B) IDs along with common identifiers and the geometry definition of each. Because it has the geometry defined, if you were to insert these results into a table you can then review them in your map.
SELECT WHYDRANT.OBJECTID AS HYDID,
WFIREDISTRICT.OBJECTID AS FDID, WHYDRANT.UNID AS UNID,
WFIREDISTRICT.UNID AS FDUNID, WHYDRANT.SHAPE
INNER JOIN WHYDRANT ON
WFIREDISTRICT.SHAPE.STContains(WHYDRANT.SHAPE()) = 1