This will be on her 2022 W-2 if actually being paid in 2022.
Because money contributed to a qualified retirement plan is still considered earned income, it is subject to social security and medicare tax, even if it is exempt (or pre-tax) from income tax. For example, if her vacation payout is $5000, one of two things could happen.
1. The school puts $5000 into the 403(b). Box 1 of her W-2 shows zero, but boxes 3 and 5 show $5000 of SS and Medicare wages. Box 4 and 6 show $310 of SS tax and $72.50 of Medicare tax. The school will ask your mother to pay these taxes back to the school (since they should have been withheld but weren't.)
2. Or, the school reports $382.50 of taxable wages in box 1, $5000 of SS and Medicare wages in box 3 and 5, and $310 of SS tax and $72.50 of Medicare tax in box 4 and 6. The school pays these taxes from her taxable wages, so the check amount nets out to zero. And $4617.50 goes into the 403(b).
She will need to confirm with HR exactly how they will handle the payout.
