This will work, although tedious and somewhat hard coded, meaning that if the dates change, the union query would have to be modified. You will need to create a separate query for each letter and then do a union on the results.
First Query--
TRANSFORM First(Table1.A) AS Data_A
SELECT "A" AS Category
FROM Table1
GROUP BY "A"
PIVOT Format([Period],"Short Date"

;
Second Query--
TRANSFORM First(Table1.B) AS Data_B
SELECT "B" AS Category
FROM Table1
GROUP BY "B"
PIVOT Format([Period],"Short Date"

;
Third and beyond...--
(Same as above but with next letter)
Final Query Union-- (Union all the queries)
SELECT qryCrossTabA.Category, qryCrossTabA.[7/22/2003], qryCrossTabA.[7/23/2003]
FROM qryCrossTabA
UNION
SELECT qryCrossTabB.Category, qryCrossTabB.[7/22/2003], qryCrossTabB.[7/23/2003]
FROM qryCrossTabB
UNION
SELECT qryCrossTabC.Category, qryCrossTabC.[7/22/2003], qryCrossTabC.[7/23/2003]
FROM qryCrossTabC;