Q:

What did Moritz Ormai forge and what happened to him?

In October 1910, the Austro-Hungarian embassy requested that the United States extradite a certain Moritz Ormai, the charge being forgery. The request was granted, as noted in this letter to the US State Department, dated October 11, 1910:

With your valued note of the 8th instant, serial No. 596, your
  excellency was so good as to send me a warrant for the surrender of
  Moritz Ormai.

There's a footnote for "serial No. 596" but simply says "Not printed." The letter also mentions that Ormai may have

committed other crimes that come under the provisions of the
  extradition treaty

and that

The royal Hungarian ministry of justice is gathering the evidence in
  the case

Then, in a letter dated October 21, the request for an additional warrant was dropped:

I have the honor to inform your excellency that my Government has
  given up extending the request for extradition of Moritz Ormai to
  other crimes and that said person was embarked yesterday.

That appears to be the final mention of Moritz Ormai in the communications between the Austo-Hungarian embassy and the US State Department. Copies of these communications can also be found, for example, here.
The application for a second warrant seems to have been out of concern that the first would expire before Ormai could be shipped back to Austria-Hungary. Given this, and that extraditions are not usually for what governments consider to be minor crimes, it seems that the Austro-Hungarians were very keen to get their hands on Ormai. The extradition seems to have been done under the terms of the Extradition Convention Between the United States and Austria-Hungary; July 3, 1856, which states that extraditions could be for

...murder, or assault with intent to commit murder, or piracy, or arson,
  or robbery, or forgery, or the fabrication or circulation of
  counterfeit money, whether coin or paper money, or the embezzlement of
  public moneys...

Curious as to what Moritz Ormai forged and what other crimes he was suspected of, as well as what ultimately happened to him, I did some googling but found no other mention of this individual online (results simply gave me lots of links to ‘St. Moritz’ and to the Italian word ‘ormai’, meaning ‘by now’ or ‘almost’).
What did Moritz Ormai forge and what happened to him? Currency forgery seems a possibility, but I can find no evidence in support of this – or any other information about him.

A:

Only partial, but we'll get a bit closer with this info:

Subsequent to the date on which the Austro-Hungarian Ambassador requested the extradition of Moritz Ormai on charges of forgery and uttering of forged papers, it was ascertained that the accused was a deserter from the military forces of Austria-Hungary and that in the circumstances it would be necessary to try the accused before a military court. When this fact was brought to the attention of the Secretary of State by the Austro-Hungarian Ambassador, the Secretary replied that

the Department understands from your note that Ormai will not be prosecuted on the charge of desertion, but will be tried for the offense for which this Government granted his surrender, namely, forgery. It is assumed that, if the occasion should arise in the future, the Government of Austria-Hungary will offer no objection to the trial before the military courts of the United States of a fugitive surrendered by that Government to the Government of the United States.

Secretary Knox to Ambassador von Hengervár, Apr. 17, 1911, MS. Department of State, file 211.630r5/5.

Since he was listed as deserter it seems most probable that they also wanted him for forging identity papers?
Unfortunately the actual warrant doesn't come up in the records of the Office of the Historian. But then not even German or Hungarian Wikipedia seems to know Ladislaus Hengelmüller von Hengervár.
It should be listed in
Extradition Warrants, 1843 - 1930, National Archives Identifier:   1229766, ARC Identifier:    1229766, HMS/MLR Entry Number:  A1 859, 5 volumes, oversized:

Scope & Content
This series mainly of copies of warrants issued by the Secretary of State for the arrest in the United States of fugitives from justice and for their surrender to representatives of the appropriate foreign governments. Also included are copies of Presidential warrants authorizing and empowering agents to receive prisoners from foreign countries and to deliver them to officers of the proper State of the United States. Each warrant indicates the name of the fugitive, the nature of his crime, and the name of the country requesting the extradition. Each volume contains an alphabetical index to the warrants by name of criminal.

