For Moms Who Know About Kittens

So , my husband and I recently moved out of our old place into a new one. were still young and trying to get on our feet so the place is really a room behind my parents house (for now) when our baby is born we will have something better. but I have a question about our kittens pooping . 
well hes 4 1/2 months 
and ( he was trained to go in the litter when we got him) so we have his litter inside our new place the thing is the place is kind of small and 
he pees in the litter but he wont poop in it and I get worried :/ because at our old place he would poop a lot in it could it be that since he had his own little room he felt comfortable? 
I hope he knows its okay to poop in there! How do I make it more comfortable for him ? Should I dump out the litter and put in fresh one ? 
Side note: now that hes getting older he likes to play outside so we let him go outside ( supervised of course and he also has his shots , but he sleeps inside with us all the time) my mom said he obviously poops outside but the thing is im always keeping a close eye on him and havent seen him poop. I'm not saying he doesn't poop outside but im just curious why doesnt he poop when hes in our room , in his litter box ?