Is it permissible for a wife to use stratagem through her husband’s social media accounts, and impersonate him to speak to girls, in order to deter them from him and prevent him from the sin of speaking to them, without his knowledge?

Spying on one's husband is forbidden (haram (definition)), and it is not permissible to seek out his faults. This action will not deter him from forbidden acts, because he can use alternative accounts. This method is not considered legitimate in deterring him. The wife should remind him, advise him, instill in him the fear of Allah, warn him of His punishment, and forbid him from evil as much as possible. Her duty is to advise him, remind him of Allah, and pray for his guidance, and she is not responsible for whether he becomes guided.