I think what you want to write is actually a Letter of Commendation. These are used to acknowledge performance beyond expectations. A Letter of Recommendation would be written if you were recommending the person for a position, or promotion.
These are generally written with a specific position in mind. Either of these letters is typically written to the manager which the person is either being commended works for or the person who will be the decision maker for the position being recommended.
In general it is not appropriate to provide a copy of this letter to the person actually being commended or recommended. It is generally an honor left to the manager to present a letter of commendation to the person(s) being commended.
Another option is to write a Letter of Recognition, or Letter of Reference. Either of these are appropriate to provide to the subject of the letter.
In the case of the letter of recognition I would generally copy the manager of the subject. A letter of reference may be written as a general recommendation but not for a specific position. A letter of reference will often carry less weight than a letter of recommendation.