Question: The condition that exists when a contract is made with the purpose of benefiting the third party?
Disambiguated questions and answers: question: The right that arises when a contract is made with the purpose of benefiting the third party?
The condition that exists when a contract is made with the purpose of benefiting the third party and third party accept the benefit?
answer: ius quaesitum tertio
right to sue
acceptance
Natural Questions answer: ius quaesitum tertio (from the Wikipedia article "Third-party beneficiary")