Is It Okay to Omit a Short Job Stint Due to Health Issues When Applying for New Roles?

I worked for Company A for 2 weeks, but due to health issues, I had to resign. Now, I want to join a new company where it does not matter whether I have any experience for my PF account. My previous company said it's okay not to mention it, and even if they find out, it won't create any problems. However, I am now confused because what if the current company finds out about it later when I join? Please suggest what I should do in this case. Would providing an internship completion certificate for those 2 weeks be okay? Thank you.

If you were a member of the PF in your first organization, it is advisable to disclose your previous employment information. Even if you cannot provide a certificate for the two weeks of experience, it is not a significant issue given the short duration. Be prepared with documents regarding your health issues to address any questions about your brief tenure at the first organization.

Since I have a service history of working in previous organizations, the second organization will definitely find out. Will providing documents regarding health issues solve the problem? Is there any chance that the present HR will continue asking for proof to know my last day of working? It's been only a week since I resigned, and the previous company hasn't yet marked my exit from their company.