The group has raised its interest in the well to 18.5% from 16.5%.
Stanley-2 is the next well to be drilled as part of a strategic alliance with Baja Oil & Gas and is the second recent well to be drilled at the Livingston Oilfield Polk County. The first well to be drilled was the nearby Stanley-1, which started in July.
Mosman said Stanley-2 is supported by information from Stanley-1 and Baja's interpretation of 3D seismic data.
Chairman John W Barr said: "Given the significant results of Stanley-1, Mosman is very pleased that Stanley-2 is now ready to get underway.
"The clear intention is to increase production and thus cashflows as quickly as possible whilst taking into account operational and legislative requirements."
The primary target of drilling is the Yegua Sands at about 3,800 feet. Several secondary targets will be tested, similar to those that were tested in the Stanley-1 well.
The drilling programme at Stanley-2 is expected to cost US$400,000. A further US$150,000 will be required for completion if the well is commercially successful.
Mosman will use existing cash resources to fund the well.