Form I-90 is what you file to correct it. Google for "form I-90" to find any comments about how long it takes.
However, because you are required to send in the old card to get a new corrected one, you should get your passport stamped to show that you are a permanent resident.
Make an Infopass appointment to go to a local Immigration office, taking the passport, form I-90, and your current card with you and ask them to stamp the passport.
---Local USCIS will not stamp the passport they need I-90 filing reciept and then stamp the passport. it seems to me that poster GC is family based and he can Efile the I-90 and pay the fee and will get I-90 filing reciept and with that reciept he/she should go to local USCIS with infopass then get his/her passport stamped.
If needed, you should be able to send the colleges a copy of the passport stamp.