Pumping milk for my preemie storage question!

My baby girl decided to come a month early, she's currently in NICU and is doing great. As far as pumping my milk, i know in order to mix the milk together into one container they both either have to be room temperature or refrigerated.

Can i mix 2 different times of milk into one container to be able to take it to her or does it have to be all separated? let's say i pumped at 10am i put it in the fridge and i pumped again 3 hours later, put it in a different tube in the fridge and later on put them in one tube together once both cold.

I know this is okay for full term babies but i'm not sure if it's the same for preemies?

Thank in advance! ❤️