H1 transfer or new H1 doesn't make any difference to you because your employer is a university/college. You need to be in a valid non-immigrant status or within its grace period when filing the second H1. If your non-immigrant status has expired and current legal presence is based on the pending H1 petition, your new H1 change of status may (or may not) be denied, (you will know by looking at the H1 approval notice, whether or not H1 I-94 is attached on the notice).