Now that BVAInet has uploaded the mbd version, I can see the problem(s).
First your design of TBLLicNo is not quite right, you should have these fields
add new field LicNoPK, select 'autonumber' as the datatype and set it as the primary key.
Delete the 2 name fields and add a new field, call it StaffID and select 'number' as the datatype
Keep the Lic#1 field but change the name to LicNumber, select 'text' as the datatype
delete Lic#2 & Lic#3 as these are NOT needed
Lastly change your append query so that the sql reads
INSERT INTO TBLLicNo ( StaffID, LicNumber )
SELECT TBLLicenseNumber.ID, TBLLicenseNumber.[Lic #1]
FROM TBLLicenseNumber;
so the ID field is appended to StaffID and Lic#1 is appended to LicNumber
run this as to create records for all staff the have a value in Lic#1, then run it again but select Lic#2 field to be appended to LicNumber
then a third time to create records for Lic#3
Notice this new table will now join to the original table using
TBLLicNo.StaffID ---> TBLLicenseNumber.ID
Hope all this makes sense
David