I would like to block-quote this postcard in APA style. The web site has prepared references citation, but it doesn't use the author's name which is clearly shown in the image itself. And if I'm not supposed to use the original author's name in the references citation, how do I format the in-text citation?
Forget for a moment APA style and ask what a citation is: A way for a reader to find the source you used so that they can check themselves. APA and other styles provide sort of a general format to do this, but the essence and end-all is not that you slavishly follow the style, but that you follow the spirit of making a resource retrievable with the information you provide.
In the current context, that means that whether or not you provide the author's name doesn't really matter: Knowing the author doesn't help anyone find the postcard. So just go with what is suggested on the website to cite the document.