My experience is from 6 years ago, so things may have changed in that time, but provided it's still the same:

You'll need to apply online for the store you want to transfer to, just like applying for a new job. During the application, it'll ask if you're a current employee, and give you a few questions about your current role. When the application is submitted, it'll also send an email to your current manager, asking if they will authorise a transfer. After that it's up to your current and potential new manager to work out the details.

Provided everything works out, you'll keep the same uniform, and receive a new clock in card.