How to lookup duplicate values between sheets and replace with value from another column

See attached sheet:

Sheet A has a list of ID numbers
Sheet B, Column A has a list of ID numbers that were considered temporary
Sheet B, Column B has the list of ID numbers that the temporary ID numbers need to be changed to
Not all numbers in Sheet B are in Sheet A.
If not in sheet A I don't want them to transfer.
Thanks ahead of time.

ID Test.xlsx

In Sheet A, Cell B2, use:
=VLOOKUP(A2,'Sheet B'!$A$2:$B$100,2,FALSE)
Copy down.

That will highlight the IDs in Sheet A that need to be replaced by the new Values from Column B in Sheet B.

In Cell B2 of Sheet A

=IFERROR(INDEX('Sheet B'!B:B,MATCH('Sheet A'!A2,'Sheet B'!A:A,0)),A2)

Copy down

Copy column B -- Paste Special values

Column B of Sheet A now has updated IDs

Hi

In C2 of Sheet2 enter the following
=IF(COUNTIF('Sheet A'!A:A,'Sheet B'!A2),'Sheet B'!B2,"")
and copy down

If this does achieve what you are looking for, then I would copy Column C and Paste Values to say column F.
Then with that range selected, choose Data>Remove Duplicates and all of your blanks will be removed, and you data in the same Order.
Alternatively, if Order doesn't matter you could just Sort column F and all of the Blanks would fall to the end.