Explain fully if a project manager can ensure that whilst meeting
time, budget, resources and the performance specifications the
customer needs can be met ?

Isnt this a question about customer perception. It depends on what the
customer expectations and more importantly his perceptions of the
project are. To delight the customer you probably need to excel at
some of the criteria e.g. deliver early. Of course this could be a
disaster if he was building a plane and you turned up early with the
wing. I suppose you need to define potential customer needs. Good
communication would be paramount. He needs to have confidence that the
project is running to schedule and have foresight of the potential
problems. It does matter if you meet all the timescales if he does
know how things are going.