I dispute the Ju390 was intended as a bomber but the V3 prototype was evaluated for the role and found unsatisfactory. It was trialed in the maritime reconnaissance role. The Ju390 was always a long range transporter. A US Navy Intelligence report from 1945 details the type's performance prior to April 1944 when it was recertified at a higher take off weight (80.5 tonnes).
Range is cited as 3,960 miles with a 10,000kg payload. Keeping in mind payload can be carried as extra fuel: Payload can be traded for extra range and it often was on the Ju290 which used fuel bladders in the cabin.
However regards the Ju390's eventual fate. over the years Geoffrey BrooksArgentine author on various Luftwaffe topics shared with me what he knew. Geoffrey also researched Manfred Griehl:
Luftwaffe over America, Greenhill/Frontline Books, UK.
Geoffrey said the JU390 landed at a jungle clearing in Entre Rios provence to unload a cargo, After unloading, it flew to Uragauy. He said,
"I have seen the landing area, which is almost depopulated, relatively even, 1945farmland and pasture skirting the main highway about 60 miles east of the River Uruguay between Paysandu and Tacuarembo, this main road today being no wider than necessary to allow single file traffic in each direction. There are several villages in the area today which retain their German character in all senses."
In various exchanges he told me it was dismantled in Uruguay. Parts were dumped in the river near Paysandu.
Lo and behold, many years later, I got to know the son in law of Nazi nuclear physicist Dr Ronald Richter. Omar Depasquale. Omar told me Richter reassembled a nuclear device from Germany at Cordoba and British saboteurs bombed it in 1947.
This correlates with the Polish interrogation of SS Lt. General Jakob Sporrenberg in which he stated a bell device was evacuated from Silesia to Norway in April 1945. A declassified intelligence report of Argentina's Economic Ministry asserts that a "multi-engine aircraft arrived from Germany and unloaded A "Bell" device. Richter continued to develop a particle accelerator for Argentina's nuclear project.
Multiple different sources suggest the Ju390, ended up in Uruguay.