Why would my dog poop for one owner but not the other?

It's probably just a matter of a different routine with you.

Do you have a command to poop? Maybe your girlfriend tells her to poop in not so many words, which your dog has learned as a command. Go out with her and listen for it.

If you don't, start using one. (Mine is "go now".) When your girlfriend expects her to poop, she can watch her and say "Go now" (if she doesn't already have a phrase your dog picks up on) when the dogs starts getting in position, every time. Soon the dog will relate the command to the activity.

When you take her out, don't use the command unless you've just fed her or it's time for her to go. If you see her start to get into position, use the command.

If she doesn't poop, bring her in, and take her out again later. It will be easier when you both use the same command for the activity.

Eventually, you can get them to poop on command.

One thing I notice about your question is that you're actively encouraging the dog to poop.

If this encouragement is taking the form of praise ("Good boy! Nice job! Keep going!") then the dog is probably hearing that praise and assuming you want him to continue doing whatever he's doing at the moment, which is not pooping.

If the encouragement is happening in the form of a command ("Go now! Poop here! Get it done!") that the dog hasn't learned yet, then he's probably either completely baffled about what you're trying to communicate or he just assumes you're talking gibberish.

I suggest not giving any praise unless and until the dog does what you want (to prevent a situation where the dog sees no reason to do what you want), and I also suggest not repeating a command unless you're at least mostly certain that the dog will comply with it (to prevent a situation where the dog unlearns the command by dissociating it with the desired action).

I find that my son's dog, who works with me everyday at the office, has the same type of behavior. He has a routine, gets dropped off, I get his kibble ready and he eats and then he goes outside for a potty break. He will pee and poo for me, sometimes poo a few times, which makes me believe that my son isn't taking him enough, or he feels safer pooing for me.

If you ever notice that a dogs will look at you when they are pooing to make sure that they are covered should there be any kind of threat. Trust is a big issue because this is the most vulnerable time for any animal and they look to see if you are there to protect or shield them from a predator. Not that this is common but its "PACK" instinct. Look up why a dog looks at you while they poo to get the full definition.

my dog does this also. He's a Malamute/Lab. He won't poop for my boyfriend, who adopted him with me. I do most of the walking and training like your girlfriend does. I'm also home more. Certain types of dog have more of an individualistic and willful personality, and huskies are one. It very well could be that your dog sees your girlfriend as more reliable than you because she works from home and does most of the walking. It sucks to hear, but my dog is also picky about reliability. He legitimately will pay less attention to me the less reliable I am. He'll also start to refuse to poop when I am less reliable. You might see if you can walk her for 10 minutes every day, including your work days, and see if it improves.