Is it obligatory to report a colleague suspected of stealing a foreign colleague's phone, knowing that the officials are non-Muslims, and would reporting lead to a tarnishing of the image of Muslims?

It is not permissible to accuse someone of theft based merely on suspicion or strong presumption; rather, it requires direct observation or hearing. If your friend has confirmed his colleague's theft by seeing or hearing it, he must immediately give his testimony to help the owner of the right recover it, even if he is not asked to do so, in accordance with the Almighty’s saying: "And cooperate in righteousness and piety, but do not cooperate in sin and aggression." As for you, this testimony is not obligatory for you unless you are commissioned to do so by the original witness and he is then unable to perform it, provided that you are just and that testimony upon testimony is permissible in financial matters. If the theft is proven, it is advisable to first try to persuade the thief to return the mobile phone voluntarily.