Woocommerce how to add account details to billing address automatically

Question

I would be much grateful if you help!

I have custom registration fields that are correctly saved in database and are accessible through:

$user->['users_tel'];

But on the checkout page, if a user is logged in, I would like to show him only the 'Proceed to pay' button.

So, I have unset all the rest of the unnecessary fields that were on the checkout page, however when somebody proceeds to payment and when I receive his order in the administration panel - I cannot see his billing info.

I want to use his account details automatically to be entered into billing info, especially my custom fields that are accessible through:

$user->['users_tel'];  

and

$user['users_instagram'];

Thank you!