Baudin departed from the meeting with Flinders continuing his westward journey. He sailed up Golfe de la Mauvaise [Gulf St Vincent] and Golfe de la Melomanie [Spencer Gulf] and at Cape Adieu (west of Fowler Bay) the survey was abandoned and Baudin sailed for Sydney where Le Naturaliste had already arrived.
Winter was spent recuperating at Port Jackson, and then Baudin returned to the southern coast for a more thorough survey. Le Naturaliste was sent back to France with its scientific collections, and was replaced with Le Casuarina a locally built schooner. In January 1803 Baudin circumnavigated Ile Borda [named Ile Decres by Peron] completing the survey of Kangaroo Island that Flinders had not been able to do. While Le Geographe anchored at Nepean Bay, Freycinet and the geographer Boullanger explored the two gulfs in Le Casuarina. Near the end of February Le Geographe and Le Casuarina rendezvoused at King George Sound, and then explored the west and northwest coasts of 'New Holland', before heading home via Mauritius. Baudin died there in September 1803.
Baudin's voyage suffered many misfortunes including numerous deaths and desertions. The published account of the voyage was written by Francois Peron (who would also die before completing this work) and Louis de Freycinet, and Baudin was unable to defend his version of events. Official reports did not refer to Baudin, partly due to the personal conflicts between Baudin and members of the expedition, and also due to the political upheaval in France in the period following the return of the expedition.
Further detail of Baudin's voyage can be found on the Encounter 1802-2002 website, under Baudin's voyage.
Following this historic encounter Flinders sailed on, continuing to chart the coast, including Port Phillip Bay. He arrived in Sydney on 9 May. Here he learned that a portion of the southern coast had already been charted by Lieutenant Grant in the Lady Nelson and Port Phillip by John Murray.
The Investigator was overhauled in Sydney and Flinders sailed north on 22 July to continue his survey of the Australian coast. In the Gulf of Carpentaria the ship was surveyed because of leaks and revealed to be so rotten that it would founder if caught in a gale. Flinders decided he would need to return to Sydney and would do so by circumnavigating the continent. But first he charted the south and west coasts of the Gulf of Carpentaria in great detail. He arrived safely in Sydney on 9 June 1803.
Flinders was anxious to complete the survey outlined by the Admiralty, and in August 1803 he sailed in H.M.S. Porpoise to secure a new ship. Soon after leaving it hit a reef. Flinders sailed the ship's cutter more than 700 miles (1127 km) back to Sydney, to arrange rescue for the crew. He then sailed in the schooner Cumberland, 29 tons, for England. Small and cramped Cumberland soon proved unfit for service, needing almost continuous pumping to keep her afloat. Flinders decided to seek help at Mauritius believing his French passport would hold good. He arrived there on 17 December 1803. Le Géographe Baudin's ship, had left for France only the day before.
War had again broken out between Great Britain and France. General De Caen, governor of Mauritius was suspicious of Flinders and with the French expedition already left for France there was no one there to vouch for his credentials. Relations between De Caen and Flinders rapidly broke down. De Caen put Flinders under arrest. Flinders was detained on Mauritius for seven long years. His French passport was for the Investigator not the Cumberland, and he carried dispatches from the governor of New South Wales: De Caen considered Flinders a spy. In France the Council of State recommended the release of Flinders and in March 1806 Napoleon also approved his release. De Caen did not act upon this advice until June 1810.
Flinders sailed at last for England. He arrived on 23 October and received belated promotion to post captain. In deteriorating health he prepared his monumental work A Voyage to Terra Australis. This was published on 18 July 1814, the day before he died.
Further detail can be found on the Encounter 1802-2002 website.