MORBY: SURNAME AND SHIP

Morby was also a family name, as well as that of a ship, in the 1820s.

MORLEY: SURNAME AND SHIP

Morley was a surname as well as that of a ship in New South Wales in the early 1800s.
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Joseph Morley
According to the Sydney Gazette and New South Wales Advertiser, in May 1820 he was a constable and pound-keeper at Prospect near Campbelltown south of Sydney.
But two months later he was replaced having been dismissed for improper conduct.
The recommendation of dismissal was made to the Governor by H McArthur Esq, the principal magistrate of Parramatta.
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In March 1826, a policeman was dismissed for assaulting Joseph Morley.
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On Friday 5 May 1826, in the Supreme Criminal Court, Sydney, a man was indicted for receiving, knowing it to be stolen, a horse, the property of Mr George Morley of Sydney, at Liverpool, on the 19th ... December 1823.
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On Wednesday 10 May 1826, the name was corrected to 'Joseph' Morley who resided in Sydney, but had a farm and stock at Prospect.
The defendant was found by a jury to be 'not guilty'.
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John Morley
In July 1823, John Morris (Morley) was appointed constable at Windsor, replacing the former occupant of the position who had absconded.

MORE CONVICTS

I have found 10 more convicts with names that may be variant spellings of 'Mawbey' on the Tasmanian Archives and Queeland State Archives databases.
MEABY
William arr. 1828; John arr. 1829; Richard arr. 1849; Thomas arr. 1854 (only on Qld State Library convict database)
MANBY
John arriv. 1804; Robert arriv. 1816; William arriv. 1820; Ann arriv. 1827 (Ann only on Qld State Library convict database)
MOOBIE
William arriv. 1842
MOABY
John arriv. 1826

1828 CENSUS OF NSW

The 1828 Census was the first to be taken in the colony of New South Wales, and the only detailed one to survive in full to the present day.
When I first looked at that for Joseph Moorbee, I only found his partner in crime, Thomas Beasley.
Then I found him listed as Joseph 'Morley'.
The details given about him were: age 31, GS, came to colony on the Eliza in 1822, sentenced to 7 years, Protestant, dairyman, assigned to Jno McArthur, Camden.

LANCASTER ARCHIVES ASSISTS

I recently emailed Lancaster Archives in England about Joseph Moorbee and found them to be very helpful.
They told me that they only keep the records of Lancaster Quarter Sessions, and that records of more serious offences tried by the Assizes were held by the British National Archives.
But they did have some information about Moorbee after all:

However a search of our electronic catalogue found the following entry from QJC/1, a calendar of prisoners:

          Prisoner forename: Joseph
          Prisoner surname: Moorbee
          Age: 24
          Offence: Burglariously broken and entered dwelling house to steal a gold watch and other
                        articles; also again to steal a small purse, 2s., 3 silk handkerchiefs & other
                        articles
          Hundred: West Derby & Leyland
          Place: Atherton/Tyldsley w' *
          Date of offence (if given): 19 May 1821
          Verdict if given (based on annotations on the printed calendar): Guilty
          Sentence if given (based on annotations on the printed calendar): Death, reprieved
*
Thank you, ACS Record Office, Lancashire, England.

The execution of JOHN MOORBEE at Campbell Town would have been a public one.
Public hangings in NSW were not abolished until 1855.

Coincidentally, two convicts with the surname NUTTALL, the name Joseph Morby used as an alias, were transported to New South Wales as convicts.John and Mary Nuttall arrived in 1801 and 1804 respectively.
They were both tried in Lancaster, in 1800 and 1802, and both sentenced to 7 years.