It's not clear what you mean by the conspiracy was not a conviction although that was the states defense at trial.
If you are saying that the state incorrectly argued that he had been convicted of that or of a felony, then that would be a basis to appeal. Also, if the state incorrectly argued this as a rebuttal / impeachment to something that the defendant testified to, that would be a basis to appeal.
Your main problem may be the amount of time that has passed. You are generally required to appeal within a certain amount of time, which has elapsed.
"they want to appeal the sentence for non existing charge and/or wrongful conviciton... do you have any advice on this?"
Yes. THEY should discuss the possibility of an appeal with their original attorney to see if they are outside applicable appeal periods and whether any substantive errors can be shown to warrant the appeal.
The foregoing is for general information purposes and does not establish an attorney-client relationship.