Hi Alisky,
No, I'm afraid you're out of luck with swapping motherboards from a different phone. The space is so tight inside a phone that each model has the motherboard custom designed for it, so there's only one motherboard that will fit in an iPhone 13 Pro Max, and that's a motherboard made for an iPhone 13 Pro Max. Even the iPhone 13 Pro and the iPhone 13 won't go in a 13 Pro Max.