OnPointerExit doesn't work

I can't confirm if what you say is true but I can think of a workaround if it is true. Everytime the object is moved, check if pointer is inside/ outside the object (see: RectangleContainsScreenPoint)(or you may have custom logic). For example, if it was outside before moving and inside after moving then invoke OnPointerEnter.

Also I wonder, if pointer gets inside the object when object is moved but OnPointerEnter is not called, after that, will OnPointerExit be called if you exit normally?

It calls the OnPointerExit when I exit the original location of the element, even though it isn't there anymore.

I don't move the button itself directly, but it's parent panel, for which I update its position every frame for smooth lerping.

Really weird...

I found that if I stop the manual movement the exit event gets called immediately after.

Ok - short summary in this video: https://www.screenr.com/pquN

Hmm, I can't think of anything about this. Maybe you should report it as bug since you already have the video they will consider looking into it.