In the event that one forgot to say atta chonantanu in Maariv, they do not repeat Shemoneh Esrei (S.A. O.C. 294:1). The reason for this is because it is not necessary to repeat, as one can say Havdallah on wine.
If one comes to Shacharis, and has not yet said Havdallah, and they have not eaten anything or done any melacha yet, should they say atta chonantanu in Shacharis?
My reasoning why perhaps you should is because perhaps it is not necessary to repeat Shemoneh Esrei to say atta chonantanu, but if I am not repeating, but saying a Shemoneh Esrei which I am obligated to say in its proper time, and have not yet discharged my Havdallah with wine, perhaps it should be said.
On the other hand, perhaps Havdalla in Shemoneh Esrei is only a Maariv establishment, and is not given to be added into any other Shemoneh Esrei.
