Is this a valid sentence using "approbation" [closed]

Let's start from the first sentence you indicate.

Approbation is an uncountable noun which corresponds to the perhaps more frequently used approval, so you can ask "Are you looking for your boss's approbation?"

The verb to approbate on the contrary is less frequent (the OED for example does not list it). You can find it with the meaning of "To sanction officially; authorize" in The American Heritage® Dictionary of the English Language, Fourth Edition; it is used with the meaning of "to accept as valid" in Scottish Law; it is listed in Wiktionary with the meaning of "To give official sanction, consent or authorization". To sum up, therefore, I think that the verb is not appropriately used in your second sentence because it has a rather more formal connotation than necessary, and I would replace it with "to approve (of)".

I would say that those two sentences are technically correct. However, I've always found the word to sound clunky at the best of times, so I rarely use or enjoy it.

If I were to change anything, I might drop the "an" from your first sentence.