First, check the 1099-Misc to verify whose taxpayer id number was used - your wife's social security number or the University's taxpayer identification number.
If your wife's social security number is used, she should contact her friend's accountant. Your wife may also want to let her employer know what is happening.
Since that checks were paid jointly, explain the error and request corrected 1099-Misc be issued. The accountant will need a contact at the University to get the necessary information to complete the 1099-Misc.