A word that's between 'recommended' and 'awarded'?

If I recommend a particular website to you it means that I tell you that you should visit it or that you might find the information you want there. It does not mean that I am suggesting that you should receive it. Therefore the boss can't "recommend the Prize to Jill".

He could recommend to her that she enter the contest for the Prize but he can't recommend the Prize to her.

He can, and I think this is what you mean, "recommend Jill for the Prize" which would mean that he would suggest to the people who award the Prize that they should give it to her, but he can't do that if he is the only person who makes the decision because you can only make a recommendation to someone else, if you do something you decide to do it.

Edit: You could try "The boss gave the prize to Jill". In this context 'gave' has two meanings, the normal one of handing it to the recipient and the process of choosing one person over another to be the recipient. This slight ambiguity would soften the formality of 'awarded'. You could also use 'handed the prize to Jill' for the same reason.

I don't know if there is a specific verb that would capture what you're going for; I think you would need to add additional information to convey that the decision bears the weight of a unanimous agreement.

The boss awarded the prize to Jill, the unanimously agreed upon recipient.

The above sentence looks a little better rewritten this way though:

The boss awarded the prize to the unanimously agreed upon recipient: Jill.

I wish for a sense that it was agreed upon to give Jill the award without saying 'the department'.

If you want to de-emphasize the subject who gave the prize to Jill, then using the passive voice (just like you do here) would be a good way: "Jill was awarded the prize."

Is there a word that is between 'recommended' and 'awarded'

Perhaps commended or selected.

I don't want it to be emphasized that the boss is the only one gave it to her, but the truth is, the boss is the only one who gave it to her.

This is a very nuanced message to convey in a single sentence.