Please note that under Swiss law, the contract is valid even if it's an oral agreement. The fact that your husband worked and that this was accepted by the owner of the garage tends to prove that there was an agreement. Then, the difficult part is probably to prove what were the exact terms which were agreed if there is no written document. Did he have any exchanges of e-mails or other correspondences before he started working? If they agreed on some terms and if the work effectively started on this basis, there is in principle a contract.

Thank you for these usefull information. We do have the sms and emails that specifically describe the terms. We will wait until next week for the owner to respect his part of the contract.