Does anybody knows how could I get the plain password (via hook) in the moment a user registers and before it is hashed?
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I haven't looked into it, but any hook on the page that processes the new user registration will have access to the
$_POST data and as such you could get it from there.
I agree with the other comments above, you should be able to use use the WordPress hash and check the password on the other website. Would be more sustainable and less susceptible to alterations in future.