BOYFRIEND PROBLEMS girls !

So I have this boyfriend who is a compulsive liar. He even admitted to it. I love him and he usually good but if I put him on the spot he’ll lie. Yesterday some girl added him back on snapchat and I looked and on the chat was just a whole load of nudes he had sent back and forth just before we got together. he had even sent things to this account on the 14th November.. we officially got together on the 17th so we were seeing each other.. he had this girl who he sent nudes to on his phone about a month after but when i went on the chat he stole the phone off of me so i couldn’t look.. help what do I do?! I love him but he’s fucking up.. i want to work with the relationship and with him but i don’t know how and if I should..