I wondered what became of him. With the caveat, that I can't promise that this is not another man going by the same name, although that seems unlikely, it turns out that he had a second career in the 1860s, as a traveling miracle working charlatan with, probably, some mental illness. This inspired various people to warn people about him in the newspaper Hamaggid. The first is from Hamaggid #22 1864. As you can see, the paragraph about him is actually censored by the Czar so we can't see his name mentioned. The only way I even know that this is talking about him is because a later issue refers to this one.
Writing from St. Petersburg, someone named D. Y. Kangisser wrote something about someone - we will see that it is Danemark - and in the part that we can read at the end he says that he wanted to notify the readers of Hamaggid in Galicia - where he was apparently from - perhaps they know the man, did he leave a wife behind, for example. Once the man's identity is established, maybe then we can know what to do with this "false prophet," (navi sheker).
Now that the media began covering him, another person, named Yeruchem Fischel Ze'ev Rosenzweig, sent in a letter, which appeared in #32. He says that when he met him several years earlier, he was going by the name (Rosh Barzel/ Iron Head - we will see below that he was using the name Eisenkopf). He asked him where he was staying. He told him that he was staying in a hostel owned by a Christian woman. Rosenzweig asked him why, and he told him that at that particular time he was not there for the Jews, but to perform miracles for the Christians. Upon seeing an example of his miracles, he was singularly unimpressed. Danemark told him that he can show him that he will impress people in the local (town hall?), but he merely did the same trick. Then he began to blaspheme against Judaism and even the Christian official couldn't take it, and the people wanted to beat him. The editor of Hamaggid added a note that he had also received a letter from someone in Mogilev about him, and how he impressed and collected much money from the superstitious women and fool[ish men] in his city. The editor believes it is important to publicize this man.
Then a few issues later, Shalom Barasch wrote, from Pest. This time he said that Denmark had lived in Pest for quite awhile, and married a young, poor girl of Polish origin in his city but he had divorced (or abandoned?) her. He was saying negative things (as he apparently was wont to do) and then he saw that it wasn't winning him fans, he disguised himself, dressing like a rabbi in black. He posed as an expert in Bible, Talmud and Aramaic. When he was exposed as a fraud, he left.
Then in Kovno someone came across him at the post office. He saw a crowd of men, women and children around this person, and he was saying nasty things, calling this one a bastard and that one a harlot. He asked who the man was, and was told "A crazy rabbi." He went to the police station to see if they knew anything about him, and they showed him that approbation letter he carried, which called him "The great rabbi Hirsch Denmark from Austria." So, obviously curious, he went to the place where Denmark was staying. He saw that he was surrounded by a group of course men, he was drinking, and saying terrible things about the Jews and their faith. He asked him, To which faith do you subscribe? Denmark answered "Karaite." But a moment passed and then he began cursing the Karaite. He could see, he writes, that the man was neither Jew, nor Karaite, nor Muslim - he was just a drunk.
Finally, this last piece is from Hamevasser, published in Lemberg. It refers to Barasch's letter in Hamaggid, and says that Denmark also visited his town, and called himself Eisenkopf. After doing his miracle schtick, people asked him, what did the Rambam write, what does it say in the Gemara? He declined to be tested in this manner. He was asked if he was married, and he confessed/ claimed that he had two wives.
In any case, I do find it strange that no one seems to have recognized him from what he was up to nearlt 20 years earlier - this is a reason, I suppose, to wonder if it was the same person. On the other hand, was his nom de plume "iron head" meant to evoke the great mind he possessed, or felt he possessed? But here it is.