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You probably know this already - and if you do, I apologise - but depending on what type of Reich tap you've got, the spout may well be replaceable on its own.
If it's a Twist tap similar to this one, you can get a replacement spout Werbung: here. It's just a matter of checking that it's a push fit spout and not a screw-on one. If you twiddle it round and round and it shows no sign of coming off, it's a push fit...
As far as I can see the mounting hole is 39mm, but if you do decide to replace the entire thing, taking off the old one beforehand would provide you with a useful dry run, allow you to make sure there's nothing else that needs fixing at the same time and to measure the hole to be certain.
And there's one other thing. The microswitches in these taps don't last forever, and although they are relatively easy to replace, installing a relay in the tap's switching circuit will make it last a lot longer, prevent it burning out prematurely and cost less in parts than a new one.
It's a pretty simple modification.
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