Is it valid to pray Dhuhr behind an Imam who is praying Asr?

If a person prays Dhuhr behind an Imam who is praying Asr, there is no harm, and his prayer is valid according to the preponderant opinion, based on the Prophet's ﷺ saying: "Indeed, actions are by intentions, and every person will have what he intended." There is no authentic narration from the Messenger of Allah ﷺ indicating the necessity of the Imam's and the follower's intentions being identical; each has his own intention.