There are two factors that come into play here. The legal principles that arise are fraud and an enforceable promise.
A fraud occurs when one party tricks another basically. There are five elements; false material statement, knowledge the statement is untrue, intent, justifiable reliance by the victim and injury to the victim.
The crux of this case will revolve around the first three parts. More would be needed to prove it in a court of law, but the assumption is going to be the promoter never intended to give the money to charity (but it doesn't really matter, more on that later). The last two are the easiest to prove. The charity had a justifiable reason to rely on the statement and they were injured due to the expenses of building the new building.
The first three would seem like a sticking point because it appears impossible to show the promoters intent. However, the law can enforce promises as an implied contract when there is an agreement and exchange of service of value. The promoter promised the charity proceeds which the charity accepted. The promoter then provided the concert and made money. The question would be what, if anything of value did the charity supply? The answer is their intellectual property of the charities name, logo, etc in the promotion of the concert. Therefore, the court can enforce the promise as an implied contract.
The charity may persuade the local jurisdiction to file criminal fraud charges in hopes of gaining restitution via the criminal process or sue the promoter in civil court for a tort, violation of implied contract.