Yes with the AMHR I have sent in a signed transfer of ownership and a request for duplicate cert with the appropriate fee with no issues. HOWEVER this horse has changed hands not once, but twice, so if the horse is still in the breeder's name, you probably need the breeder's signature on a transfer in order for it to be valid, as they should be the owner on record. If you have a transfer from the breeder to the first owner (the person from whom you bough the horse) and then a transfer from the seller to you with all of the necessary signatures, AMHR should print you the duplicate cert and it will have all of the changes of ownership listed.
It could be possible that the breeder sold the horse without papers for some reason, or the horse was not reg. or had cert taken away, you never know. Does the photo on the copy of the cert match the horse? Basically, the important thing is having the signature on the transfer matching to the owner on record with the office. It is not entirely the breeders fault, as if they gave the buyer a transfer and the buyer (the seller in your case) never paid for a duplicate. Many breeders and sellers invest as little money as possible into sale horses and there may be a reason this horse's papers never were issued. If someone here with access to the stud book can help you look the horse up in the appropriate registry they will be able to tell you the owner on record. If you get the owner on record's signature, you should be able to get a duplicate. Ask one of these nice people to do a look up for you. They will need the horse's registered name/number and appropriate registry. good luck.