@Monquito:
The thing is, white amber was a lot more complicated than his actual lost limb, he's a genious on surgery, just look at actual Brownbeard, attached some crocodile or whatever the reptil it was to him and make it work, he can reattach his arm on his own, Doula definitely knows this and that's why he did an unclean cut, which would only complicate Law to put his arm back but won't stop him from doing it.
You have no idea how complicated or simple white amber is. Maybe you're right, but maybe you're not - we just don't know.
@Monquito:
Which proves that he can reattach limbs and make them work.
Actually it doesn't prove that he can attach limbs. It may suggest it, but that is debatable. We have not seen Law give anyone a limb - or attach - any limbs. All we have seen him do is swap limbs; apparently, he can spatially manipulate matter within his rooms - he can exchange their spatial coordinates with those of other matter. He did not attach any crocodile legs to brownbeard, but swapped his non-working legs with crocodile legs. The same holds for all the other centaurs and whatnot on punk hazard. When teleporting at Doflamingo, we saw him throw a rock (or something) and switch places with it. The only possible exception I can think of is when he teleported through a wall on Punk Hazard, but that is still a long ways away from proving that he can (by use of his fruit) attach one piece of matter to another, rather than merely being able to switch one piece of matter with another.
But, I expect the sewing fruit will come in handy here. Even if sewing it up won't actually make it work again, you are probably right about him being able to make them work again - swapping brownbeard's legs with working crocodile legs is probably quite a feat, but he was able to do it.
I guess the questions are:
(1) Can he attach matter to other matter, or just swap matter with other matter?
(2) Is he capable of making swapped limbs work, or do the limbs have to be working to begin with (e.g., if he took working crocodile legs from a crocodile and gave them to Brownbeard, would he have to manually make sure they were hooked up right and worked or would they continue to work via DF magic?)?
Also, we need to think about what it means to "heal."
It seems like Law "treats" or "cures" things, but "healing" seems more like a regenerative process internalized within some agent or object - in other words, it isn't a matter of going in and removing something, but rather a matter of the thing itself regenerating itself.
I'm not sure a lost arm could be "healed" as it is now distinct from the body that lost it, and the body has no capacity for regenerating an arm.
Then again, the whole "heal the smile factory" line messes everything up… Again, just too many unknowns to Mensherry's power. It sounds more like a "restoration" fruit. In any case, Law does not "heal" in the sense of regeneration or restoration, or in any sort of internalized procedural sense by which his power is a catalyst for some thing's "healing;" rather he goes in there and metaphorically (sometimes literally, I bet), gets his hands dirty and actually moves things around or removes thing. I'm not sure I'd call that healing.
It doesn't matter anyway, since all we are arguing is semantics. I think someone had an oversight as to possible extensions of the term "heal," and the whole debate is just one about illegitimate use of a word. In which case, who even cares?