At the age of 16, what exactly was James Vaux accused of stealing to get him a sentence of being deported to Australia for 7 years?

Assuming that this is James Hardy Vaux (1782-1841), the item in question was a handkerchief, valued at elevenpence.

https://adb.anu.edu.au/biography/vaux-james-hardy-2756

James Hardy Vaux was a professional thief and swindler. He ordered goods from vendors which he never paid. He moved out of his lodgings late at night to avoid paying his debts and rent. He collected donations which he used for himself and stole money from employers. The handkerchief case was just the last straw.

The seven year sentence he received was not his last. He faced a second and a third transportation to Australia as he never refrained from his dishonest activities once he came back to England

https://en.wikipedia.org/wiki/James_Hardy_Vaux