Yes, but the cost (basis) of the vehicle when added to B will be the ending basis from A (if there was no overlap of business usage between A and B). On A in TurboTax you will report that the vehicle was switched to 100% personal use and leave the sales price and basis for gain/loss blank. When you add the vehicle to B you will report the purchase date as the true date you bought the car (2020 or earlier according to your post) and the amount you paid for it. You also need to determine the Fair Market Value of it on (around) the day you started using it for B.
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