If people with truncus arteriosus type 4 receive a heart transplant will it solve the problem?

No: Type 4 truncus arteriosus is also known as pseudotruncus. It is typically repaired surgically, not with a transplant. If a patient has a failed surgical repair a transplant is sometimes an option. A transplant is not a cure, as it is a medical condition itself that has to be managed closely. Rejection is always to be feared, and anti-rejection medication can have troubling side effects.

Yes: The truncus is replaced with aorta and pulmonary artery to proper connections.