Legal Question in Business Law in Texas

That's a rather loaded question, and there are not enough facts to get the answer you're looking for. Was the credit card authorized on behalf of the business pursuant to the bylaws/operating agreement/partnership agreement/etc? Were the debts on the account for business reasons?

To address what I can:

The partner that used his own information to obtain credit on behalf of the business has more than likely personally guaranteed that line of credit. Therefore, that partner is "on the hook" should the business fail to pay.

As for "sole" responsibility, that's up for debate. He likely entered into credit on behalf of the business. Assuming the debts used on that line of credit were for business purposes, and the business authorized the line of credit, the business should be first in line to pay. Therefore, the business "should" pay the debt first.

If the business doesn't pay the debt then the credit grantor will look at the personal guarantor. (It could sue the business, but rarely does--they usually go after the guarantor directly.)

The guarantor would then have the ability to sue the business for failing to pay.