Learn me please: Lease take overs

So long story short, I have been trying to buy my coworkers 2020 Miata Club since about mid February. He is leasing the car through Mazda North America. Initially, Mazda told him that they do not do leave transfers. With that information, I was prepared to pay the seller an agreed purchase amount so he could in turn buy the lease out and "sell" me the car. I applied for financing through Navy Fed and got a great rate because they classified the car as "new". They cut me a check with his name on it.

Fast forward to today. Due to work scheduling and him testing positive for COVID, I was able to finally able to speak to him at work. He said that he had spoke to Mazda yesterday about the situation and come to find out, they DO allow lease transfers. The Mazda customer service rep stated that he would have to pay sales tax when he bought out the lease and that I would have to pay sales tax when registering the car in my name. I know he didn't want to pay sales tax to just sell the car to me so I am open to taking over the lease. However, I still have a $27k check with his name on it. I'm sure I can talk to Navy Fed and basically cancel the purchase as I have not made any payments on the loan yet (1st payment was due 12 May).

The Mazda customer service rep told the seller that they are mailing him the leasing packet. He told me that they will require a credit check.

How does this process work? I have never taken over a lease before, only purchased a car with financing or with cash. I'm in Florida so if anyone has experience with any fees or taxes that I can expect, that would be great! I was fully expecting to buy the car with financing but can I buy out the lease after I take over the lease? I'd rather own it than lease it as the mileage limit is only 10k miles and I was planning to sell my truck and have the Miata as my only vehicle.

Lease buyout:

When I buy out leases to resell I don't pay sales tax. It's state dependent 

in ca - person who leased pays tax only on monthly payment 

so when they buy out - or I buy the lease - there is a window where if you resell it there is no sales tax for me. I am middle man. New owner has to pay sales tax. 

not sure your state laws 

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transfer on lease. I just transferred my corporate lx570 lease to new owner. Depends if it's captive or non captive, new owner went through credit check with bank. They paid transfer fee. Lease moved from my LLC to the new owner. I didn't have to do anything. Once approved I gave them the key 

In reply to mr2s2000elise :

Thanks for the info. Since the lease is through Mazda, I'm assuming that they are the ones that will pull my credit? To be honest, I'm kinda nervous about that because I don't have great credit (~670 or so) and I got rate through Navy Fed on the loan.

Since the current lease is through Mazda Financial Services (its actually through Toyota Motor Credit Corp; Toyota handles financing for Mazda), I'm guessing the current lease is a captive lease? Can I get lease financing through an outside financial institution (like Navy Fed)?

One last question: Assuming I can actually take the lease over, can I buy the lease out at any time or does it have to be at the end of the leasing period? Truthfully, I'd rather just buy it than have to deal with the mileage and service restrictions tied to the leasing terms since I plan on selling my other two vehicles and using the Miata as my only car. Auto insurance is ridiculous in Florida and having more than one insured vehicle is like lighting money on fire.