Kinda yes/no probably no.
The LA valves were quite different to the Fullerton valves there was a radical change to the guides that forced changes to the valves.
Most of the Ambassadors available are Fullertons and therefore unsuitable for an LA Special
Even during the LA period they changed the guides which changed the valves.
The result is you would have to buy an LA Ambassador to have any hope of valve compatibility between an Ambassador and an LA Special and both would have to have the exact same late LA valve design.
There are also differences between the early LA valve stem and late LA valve stem that would require the valve and the stem and maybe other parts to stay with the valve they came with and they may make the valves incompatible as well.
For example the early valve stem not only is a different length to the later valve stem but also has a different fixing to the valve so you have to use the same stem that comes with the valve and the chance of vertically aligning the valve is therefore slim.
This site shows the issues
https://www.robbstewart.com/olds-early-trumpets
The LA Ambassador uses the square shaped bar as a valve guide, if your Special has the same square shaped bar then it might be physically compatible with an LA Ambassador.
LA Ambassadors are quite rare and carry a premium cost.
Even if they are physically compatible the port positions are likely to be wrong anyway.
To put this in perspective an LA Ambassador may be a bit cheaper than a LA Special but will come with a heap of uncertainty and possibly extra costs on top so I would not even consider replacing an LA Special valve with an LA Ambassadors valve and have the extra risk.
You are probably better buying another LA Special and you will then know the valve will fit and you can use whichever instrument plays best. Additionally if the one you choose develops a problem you can simply swap the third valve over and have a second instrument. It would be as close as possible to a zero cost fix.
It just wont be cost effective to try to get an Ambassador valve to work in my opinion.
And you wont know the condition of the Ambassadors valve before you see it and that may come with issues as well.
You have not said why you need a replacement valve perhaps it might be fixable by a tech at far less cost than trying to source a suitable Ambassadors valve if that were even possible.