If the client has an unused Tuition fee from the previous year, can he still transfer it to their spouse?
No. Amounts can only be transferred in the year they are received.
Here’s some additional information on this:
Line 32600 – Amounts transferred from your spouse or common-law partner - Canada.ca
I was thinking the same, but TC transferred $5000 from BCS11 to the spouse last year. Now my client has to pay it back.