Is it permissible for an employee to submit a proposal to carry out work for their company through an external party, even though this work is not part of their duties, and it achieves financial savings for the company?

If the submitted offers are not confidential, and you are not obligated by contract to perform this work, and it does not harm anyone, then there is no objection to submitting a lower offer to the company than what was received, whether directly from you or through an external party.