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if you don't own the property you can't depreciate it (see discussion of lease-purchase-option). 

this comes straight from IRS PUB 946

You can depreciate most types of tangible property (except land), such as buildings, machinery, vehicles, furniture, and equipment. You can also depreciate certain intangible property, such as patents, copyrights, and computer software.
To be depreciable, the property must meet all the following requirements.

It must be property you own.

if your agreement does not have a valid Lease-Purchase-Option (as determined under the tax laws) the agreement for you to take depreciation has no validity under the tax laws

 

if the lease has a lease-purchase-option then if it meets certain criteria it would be treated as a sale by the owner upon the agreement going into effect and you would be treated as the owner eligible to depreciate it.  two important features of an LPO

these factors indicate that a tenant is acquiring an equity interest in a property:

payment of rent in an amount that is substantially in excess of the actual fair market rental value of the property; and
the sum of the rent payments and the option price approximate the fair market value of the property.

 

see the discussion. 

https://www.ccim.com/cire-magazine/articles/lease-option-or-installment-sale/#:~:text=The%20tenant%2...