Hi Florian,
Thanks for your suggestion. An option labelled " Save card for faster checkout in future" is displayed to clients when the "Allow Client Pay Method Removal" option is enabled in your General Settings > Security tab: https://docs.whmcs.com/Security_Tab#Allow_Client_Pay_Method_Removal

This will work for any card details stored locally by WHMCS. It does not apply for tokanisation gateways where the card details must always be stored by the gateway provider.

And you can also customise the appearance of the checkout.tpl template to add any messaging you may require: https://docs.whmcs.com/Order_Form_Templates