Is imagining having intercourse with someone upon waking up with high lust, while it is involuntary, considered Haram, and what is the solution?

It is not permissible to conjure up sexual fantasies and derive pleasure from them. However, if they occur without being sought, there is no sin in them, but they must be repelled so that they do not lead to corruption and temptation, for they are the root of all corruption, as Ibn Al-Qayyim explained. A woman may offer herself to a righteous man for marriage, with proper regulations and manners.