There is a source, but according to this source, the story is only half-true. As is described in the link you posted, the story took place during the Austro-Prussian War of 1866. The contingent was stationed in Southern Tyrol, where they were supposed to guard the Austrian/Liechtenstein border against Italian troops.

Once the war ended, they were called back to Vaduz, Liechtenstein's capital. While in the field, they had been given an Austrian liaison officer named Radinger, who stayed with them on their march back as an official escort.

So yes, they did return with an additional soldier, but he was simply an Austrian liaison officer, who I'm sure returned to Tyrol soon after.

Source: Historisches Jahrbuch Liechtenstein, Volume 24 (1924)