The project manager should work with the client on an acceptable amount of time for document approval, as this is the best way to address the issue of slow turn-around times and avoid potential delays in the new project. By collaborating with the client, the project manager can establish a mutual understanding of the expectations, requirements, and constraints of the document approval process, and negotiate a realistic and feasible timeline that satisfies both parties. This will also help the project manager to build trust and rapport with the client, and foster a positive and cooperative relationship.