Maximus are not likely to know anything about you, other than what you have told them in your ESA50 and supporting documents. They won't even know whether you are already in receipt of ESA, certainly not whether you also have a live DLA/PIP claim.
You can send in the PIP decision letter if you believe it to be helpful. However, you should also show how it is relevant to your ESA claim. For instance - PIP and ESA both have 'mobility' descriptors but the actual criteria are very different from each other.
Nothing on this board constitutes legal advice - always consult a professional about specific problems