The user. Unless the software was purchased under some sort of alternate site license, it is only licensed for single users. A school or band booster program is unable to "own" a single-user license since they are not a singular person. This is important to understand in cases where a staff member leaves a school program. Even though they may no longer be with the school, they are still the legal owner of the license and any new staff members would have to obtain their own unique license (serial number) by purchasing it.
Plainly put, it doesn't matter who initially paid for the product. The registered user is the one who actually owns the license.