Rabbitsfizz(and others)are right; it would be best to simply(and anonymously, if you wish, provide the documentation from the other breed association/registry. Official actions should be a matter of record(even in AMHA, on the RARE occasions when disciplinary action is actually taken, in recent years,at least, it is published in the breed publication(as it should be!);this was also true years ago when I was still getting the QH Journal, and the APHA magazine.
I would encourage you to do just that; however, that said, I sadly doubt if it'd mean that such a person would be denied entry as a member. It doesn't appear to me that there is any reciprocity of any sort between horse breed registries/equine associations to try to ensure that a bad apple, tossed from one, doesn't pop up in another. IMO, though, once action(suspension, lifetime banning, etc.)has been taken, there SHOULD be a record, where anyone who wished could check to see if someone they are considering doing business with is listed!
It would not be a bad idea at all, when considering sending a horse to a 'trainer', to ask for verifiable proof of their 'horse history'-i.e.,asking what horse-oriented associations have you been a member of, and for how long; who, if anyone, have you apprenticed/studied under(and what is that person's reputation),how many years, and what kind, of experience do you have, and similar questions. Then, VERIFY their answers. If they don't want to answer such questions, or your inquiry turns up problems--RUN!
(There was a case several years ago where several 'big names' in the H/J world (USEF, formerly the AHSA)who were actually suspended for their proven parts in an insurance fraud scheme-long story short, they had KILLED healthy horses for the insurance proceeds, among other horrible things!. At least one of them is nearing the time when that person can apply for reinstatement; however, there is a petition circulating that these people NEVER be allowed reinstatement(into USEF)--and I sincerely HOPE that the petition is successful! Word is that at least one of the 'bigger' names involved again has clients(unbelievable, to me!), and badly wants 'back in'--may H*LL freeze over before that is allowed, is all I can say!!)