It's amazing how many customer service problems occur because everyone assumes everyone else is doing their job correctly. If I take a call from a customer who really needs some information from my co-worker Mary, I might be tempted to assume my work is done once I give Mary the message, "Customer A called with a question with you."
This is true if Mary calls the customer back right away and provide the answer. But what if she doesn't call? Customer A spoke with me, not Mary, so it would be my fault. Or worse, Customer A will blame all of us.
A better approach that prevents problems is to accept responsibility and be the "point person" for your customer. This can work a number of ways, but all of them result in you ensuring the customer is taken care of.
Example 1: Get the answer from Mary and call the customer back yourself.
Example 2: Do a warm hand-off. This involves making sure Mary knows you've passed the customer along to her and the customer knows Mary will be responding to his question.