Is there a noble Hadith to the effect: "When a man reaches seventy years of age, his evil deeds are transformed into good deeds, and when a believing man reaches ninety years of age, Allah informs His angels that 'this is My servant, a captive on Earth, imprisoned by death'"?

Perhaps the questioner is referring to the Hadith: "No one who lives to the age of forty in Islam..." which is an Hadith that is not authentic.

There is also a different perspective on this, as a long life without good deeds is a trial, according to the Hadith: "The best of people is he whose life is long and whose deeds are good, and the worst of people is he whose life is long and whose deeds are evil."