The original German edition of
Mein Fliegerleben was printed in 1935, and included an image of Udet's signature on the front cover and introductory page. Udet's signature was, therefore, readily available from 1935 forward. As far as I know,
Ace of the Iron Cross didn't come out until 1970. I am not familiar with
Ace of the Black Cross. Check the publication date of the English translation you mentioned, the addressee of the autograph, and draw your own conclusions.
Caveat emptor!