How should I pre-cook a burger to be micrwaveable?
I think a microwaved, reheated burger is probably not going to compare favorably to a freshly-cooked burger. With that said, I think the main thing for the pre-cooking is that it would need to be start off a little undercooked, otherwise the heating process is going to result in it being overcooked (since you're saying you're looking for some pink in the middle). 

Other than that, I think the key is more in how you microwave it. Obviously, you want it to cook evenly. I'm assuming you're starting from refrigerator-cold. If you start from frozen it is going to have a lot more trouble heating evenly. Also, it might go without saying, but I'd cook the meat on its own (no bun or condiments). 

Most microwaves tend to have hot spots in certain areas. There is a pretty interesting (IMO) blog post that demonstrates this using papadam (those crispy lentil crackers you get at many Indian restaurants). The ones tested in that experiment, seemed to mostly be good directly in the center of the tray, so that might be the best placement. If you want to be really super-scientific about it, you can try to replicate that method and figure out how to arrange your food in your microwave. 

But if you don't have any papadam handy and you don't know what your office microwave is doing, you may want to find a supposedly-microwave-safe plate that still tends to get hot in the microwave and heat your burger on that. I think the plate is going to transfer heat more evenly to the burger than the microwave would. (On the other hand, I sometimes question whether dishes that get really super hot in the microwave are, indeed, as microwave-safe as they claim to be, so use caution....) Using a real plate, though, instead of a paper plate should help with the evenness of the heating.

I'd also suggest cooking it in short bursts (15s at a time) and letting it rest in between, or cooking it on low if your microwave has power settings (which just does the same intermittent power thing anyway).