They fear that the skull of Hitler's right-hand man may have already been cremated following the results of DNA tests which last week proved it was his. They accept that the skull, found on a Berlin building site in 1972, is Bormann's but insist that tests must be done on the teeth and on the earth the skull was encased in to establish when and where he died.
If Mr Bormann died in 1945 his assets would have gone to his family. If he died later, after being condemned as a Nazi war criminal, they could be confiscated from relatives.
The author Milton Shulman, a wartime member of Canadian intelligence, said that an earlier dental examination suggested the skull had had eight fillings added after 1945, implying that Bormann had survived the war. Despite being found in the yellow, sandy soil typical of Berlin, the skull was covered with thick red clay comparable to that of the Ita region of Paraguay, where he is rumoured to have died in 1959.
Mr Shulman said: "There is an argument that it is in the family's interest for him to have died in 1945, because legally he did not become a war criminal until the decision of the Nuremburg tribunal in 1946.
"He was fantastically wealthy, and if he died after being condemned as a war criminal, then any of his assets which survive could be confiscated.
"We are asking the family not to destroy the skull hurriedly ... There is serious concern about the skull, and on any reasonable basis the family should not destroy it. They have gone to the trouble of DNA tests, so why not have an independent dentist's report, too?"
Solicitors representing Mr Shulman, military historian Duff Hart-Davis and television producer Bridget Winter wrote to the Bormann lawyer Florian Besold last Friday, requesting that the skull be subjected to independent dental checks.
The remains are understood to be in the possession of the Bormanns, who would like to have them cremated and the ashes scattered at sea.