Can you store Breast Milk?

Yes you can.

Mom's Milk storage guide from www.ameda.com

Storage Time for Human Milk*	Deep Freeze (0°F/ -18°C)	Refrigerator Freezer (variable 0°F/-18°C)	Refrigerator (39°F/4°C)	Cooler with Ice Packs Frozen (59°F/15°C)	Room Temperature
						(72°F-79°F) (22°C-26°C)
Fresh	Up to 12 Months	3-4 Months	8 Days	24 Hours		4 Hours
Frozen, Thawed in Fridge	Do Not Refreeze	Do Not Refreeze	24 Hours	Do Not Store		4 Hours
Thawed, Warmed, Not Fed	Do Not Refreeze	Do Not Refreeze	4 Hours	Do Not Store		Until Feeding Ends
Warmed, Fed	Discard	Discard	Discard	Discard		Until Feeding Ends

The NICU stores the milk until needed and then measures out enough for one feeding.  Any left over in the bottle is discarded.