How is inheritance classified in Adam Smiths profit/wage/rent classification?
Profit, wage and rent are rewards for inputs used in production, they constitute a decomposition of Income (or the Income-decomposition of output produced)

Inheritance is a transfer, it does not involve production. So it is invalid to try to fit it into the mentioned classification.

Consider now any gift: say I work, earn a wage in the form of consumer goods, and give them to you. The consumer goods I got as a wage is a reward for my labor. Giving them to you is a transfer of already produced output. 

In inheritance, this output has already taken the form of assets rather than consumer goods.