I would like to find out if he can recover this money in his taxes next year.
The "imputed income" occurs when you add someone to your health insurance who does not qualify as your dependent. If he/she doesn't qualify as your dependent the amount is taxable and you can't recover it on your income tax return.
If he/she does qualify as your dependent the imputed income should not be included in your income and, if it is, you can claim a deduction for the medical insurance paid for him/her if you itemize. However, to qualify he/she must live with you all 12 months of the year, you must provide more than 1/2 of their support, and they must earn less than $4,050 in income subject to tax. If you recently became unemployed, it's likely that considering the entire year, you don't meet the underlined portion.
