I entered into a short term rent to own agreement on my primary home in June 2020 that will be sold in April 2021. We have received rent and will allocate expenses accordingly given personal use percentage in 2020. Is it necessary to take depreciation for the 6 months in 2020 and the 3 months in 2021 and recapturing in 2021 since the primary residence rent to own conversion was less than one year?
Yes. The reason is that the IRS tax law follows 'allowed or allowable' which means 'use it or lose it'. Essentially, whether you take the deduction or not you will recapture it. For this reason you need to use the depreciation in 2020 and 2021 and utilize the deduction.
To help clarify why you are required to depreciate, even though you are renting it out for less than one year, take a look at IRS Publication 527 page 6, middle column. Under "Excepted Property" it states that you do not depreciate "Property placed in service and disposed of (or taken out of business use) in the same year." So your situation doesn't meet that requirement. You placed it in service in 2020, and will be selling the property (thus disposing of it) in the next tax year. So you're required to depreciate it.