I would suggest: She gave the students permission to use their cellphones. (for a one-time exception to a policy) OR She lets the students use their cellphones. (for an ongoing policy)

I prefer "to the students" because the verb "give" most often follows the pattern: "give + something + to + someone". You can simplify the sentence by dropping one of your prepositions: "She gives cellphone permission to the students" Grammatically, there is no difference between your two sentences. Both are correct and it is difficult to detect any difference in meaning.