not the first time this happening.
a quick search in the forum and you find this forum post:
https://forum.empyrion-homeworld.net/t/npc-core-disappers/19512
and when you read the guide for the core you find this:
You CAN’T get the Alien Core back out of your structure unless you have EGS Recycle level 5 and recycle your structures !
sorry for the bad news!