Yes. Even though there is an age limit for making deductible IRA contributions, there is no age limit for making a conversion from a traditional IRA to a Roth IRA. There is no need to have earned income in the year in which the conversion is made. Of course, income resulting from the conversion must be recognized, which could impact whether and to what extent Social Security benefits are includible in gross income.
Reporting income when actually or constructively received and deducting expenses when paid. Certain businesses may not use the cash method.