It is not compulsory to send the customer offer on the same gig on which the client contacted you. You have the flexibility to change the gig if you believe another one would better suit the client's needs. However, it is important to ensure that the new gig aligns with the client's requirements and expectations. By offering a gig that is tailored to their specific needs, you can increase the chances of securing their business and providing them with a satisfactory experience.