How to distort or find a photoshop action to fit a flat seamless image to a 6 sided sphere

Hi all

I've been searching for some time to find an answer to my issue, and getting nowhere

What I need to do is this

I play a game called Freelancer, a space trading game, with planets and bases etc etc

im trying to find a way to create/update planets textures

As you can see in this video,
What I did is import a flat grid image onto a planet to check out how it works

And it came out looking weird, as you can see





With a little research I gathered that the way the game works it uses this kind of method/imaging to wrap textures/images around a planet



What I need to know/find out/ or find is a simple (hopefully) script or PhotoShop action that can distort or “shape” a flat image to match the sections of the 6 sided sphere so it won’t look distorted in game, corners match, hopefully someone knows what I mean



Is there something, a way or a program/PhotoShop action?