Mike buys for Sally, his girlfriend, a car before his trip overseas. He buys the car at Ace Autos. Ace Autos is to deliver the car to Sally within seven days. Mike signs the contract and prepays. Mike then leaves the country for his trip. Ten days have gone by and the car has not been delivered. Sally is not able to get in touch with Mike, and she calls Ace Autos. They refuse to talk to her and claim that they have a contract with Mike.
The scenario you present is interesting because it presents an important nuance.
By "third party liability" I assume you mean what is commonly referred to as the rights which may belong to a "third party beneficiary" to a contract.
Generally a third party will have the right to enforce a contract ...