Is it permissible to take a large sum of money from a bank for investment, given that the transferring party stated the money belonged to an Australian engineer who died and left the amount in the bank, and the bank agreed to invest it?

This money belongs to the heirs of its owner, and the bank is not permitted to dispose of it. Your taking it is not permissible. Furthermore, contacting someone via the internet without knowing the caller might be a deception. A believer should be astute and intelligent, not falling for the tricks of fraudsters. In the Hadith: "Indeed, Allah blames one for helplessness, but you should be resourceful. If a matter overwhelms you, then say: 'Allah is sufficient for me.'"