I guess there will not be problem to file for naturalization. As long as you have a copy of the greencard and alien number that should be okay. However, the new employer might want to see the original copy of the green card. There could be a problem without the actual greencard. However, the situation will not last for a year. Just file I-90 form to USCIS (if possible file online). Print the receipt notice. This receipt notice will be the proof for anything until you are given an appointment for finger printing and finally a new card.