For what purpose? He's lending it to the museum?
No tax consequence and no basis adjustment.
EDIT: I think you changed your OP. Now it says client donated it to the museum.
All conditions being met, client gets a charitable contribution deduction of the FMV.
If anywhere it goes to basis but, any increase in basis is usually calculated at time of sale. There is no tax return input at this point. FMV can increase or decrease over the years the item is owned.
If the client still retains ownership then there is no donation and therefore no entry. Loaning something to an art gallery or a museum does not transfer ownership as far as I know, therefore no donation.
I think you want this one, pg 11, right column:
https://www.irs.gov/pub/irs-pdf/p526.pdf
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