New born baby storing milk in cheeks

I fully direct latch breastfeeding my baby. He tends to fall asleep after drinking milk which is no issue because he empties my breast all the time. The problem is, he would always leave that last gulp stored in his mouth. He would eventually spit it out and leave milk stains. An#pleasehelp #advicepls other worry is choking. Is there any way to make him swallow the last gulp? And yes, I do try to wake him up but he will be in too deep sleep.