David Chambers, a 31-year-old software engineer living in California, will ultimately be seeking orders that he is paid out the $2.5 million, said his Queen's Counsel Jim Farmer.
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• $2.5m fight over judge's estate
Dr Farmer has argued before Justice Jillian Mallon this week that $5 million was held on trust by Lady Deborah for Mr Chambers and his younger brother Christopher.
If that argument is unsuccessful, Mr Chambers' claim will likely proceed down a different legal route, including action in the Family Court, Dr Farmer told the Herald yesterday.
Julian Miles, QC, acting for Lady Deborah, reiterated yesterday that his client and Sir Robert intended that whoever survived the other could use their assets freely.
Mr Miles argued against the contention that either an express or constructive trust existed in relation to the entitlements.
While Lady Deborah could choose to pay out the $2.5 million during her lifetime, that was at her discretion, Mr Miles said.
Mr Chambers wrote to Lady Deborah earlier this year seeking payment of $2.5 million but was refused.
Lady Deborah, in an email declining the payment, said she would provide financial assistance if Mr Chambers was in need but she did not think he was in such a position, Mr Miles said.
Mr Chambers earns US$120,000 ($176,000) a year and has savings of US$100,000, the court was told on Monday.
Justice Mallon reserved her decision yesterday.