Although you can't convert a unique ID into a phone number, your customers can. There are several ways for your customers to get this information to you. You could set up a word and web hook and ask them to SMS a confirmation message with a piece of common information, such as their username. Your web hook would be triggered when they text in and supply you the unique ID (as we always do for any web hooks) along with the username the customer texted in. From that point on, you know the unique ID associated to the account, and the unique ID is the same for the same phone number.
Another way would be to setup a word and web hook that echos the customer's Taykt unique ID to them in the response message. Your customer would then able to login to your website and update there details.
A simple example of the web hook to echo customers unique ID to them can be found on github. A running example of the service can be found on appengine. To try the service, text MYID to 82958. Messages cost 25p. To try the webhook from the command line:
curl http://taykt-demo.appspot.com/echo -d pid="MyId"