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Oil pumped is associated with the mineral rights - starting with the time you took ownership of the mineral rights - you would owned all oil pumped.
The oil pumped before you became an owned of the mineral rights - is inventory - who inherited inventory - should be decided separately by the estate administrator according to your father's will.
Also the basis of inventory would be stepped up basis - a fair market value at the time your father died - that is very important - because there will not be any taxable gain from selling the inventory.