How can we convert, customer leave previous company service and doing business with us in spite of he is so honest and happy with that service?

Building trust makes it. It happens when the genuineness in the quality is proven. Seek customers without disturbing them. By getting their attention. Naturally, it will take time. Open your product's success stories to customers. After all this, leaving their current service and switching to the new service Depends on the business and time flexibility. Thanks

A Happy and Honest customer of a company must be loyal too. Such customer normally doesn't shift his loyalty for any kind of carrot.