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If I sell Model 3 with EAP, can new owner buy FSD for $5K?

I've ordered a Model Y, which I expect to have sometime next month. I currently own a Performance Model 3 and want to sell it before then. It has EAP, with an option to purchase FSD for $5K. If I sell the car, will the new owner have the same opportunity to purchase FSD for $5K? If not, would it be worthwhile to purchase FSD in advance of selling the car to make it more attractive to a prospective buyer? If I did that, I'd of course want to net at least $5K more for the car as well.

Thanks in advance for any insight.