Hello yes you can send it at anytime before expiration , and you will have to send as well the unexpired RTD , the processing time from the date of the application, i got my GC recently and I used it to travel with my NP I didn’t have a problem entering the states but it really depends if your asylum case was based on fear of your COP government in my asylum case it had nothing to do with my COP government so i feel ok using My NP+GC
