I'm currently legally working for a US company on a special permit, I'm not a US citizen. My permit will expire this year in a few months. I'm allowed to apply for a renewal, but I learned that this will require my employer to have a certain permit code. This is a code that I did not require for my current status, but one I need only to renew it. The HR Department of my current employer told me they do not currently have this code, but they are actively trying hard to get it and apparently it's their priority. I'm really happy in my current employer and I want to give them a chance to get this permit code (as they claimed they will be able to get it before my deadline, but no promises).
In order to increase my chances of being employed in US after my current permit expires (i.e. to renew it), I plan to go on a job hunt and specifically choose a company that has this permit code (it's supposed to be an easy thing most US companies have, I don't know why my employer is having a problem, having said this I have exactly no idea what is the process to get this code). However, there are a few complications and I unfortunately, I do not have a friend or attorney that can help me, so I have these questions:
Should I share this concern with my manager? Currently only HR knows, not my manager. I do not want to be fired right now just because my immigration status is wacky. I have a very good relationship with my manager and he has "big plans" with me (and I recently received a huge and generous bonus).
What's the best way to filter companies that match my criteria? Is this something I can straight-up ask in an initial screening? I do not want to come off needy or "weird", so to say, but I guess companies understand that employing non-citizens do require special complications.
I'm a little time pressured. Not too pressured, I still have a couple months to find a new employer and apply for a renewal; but I'm wondering if it makes sense to quit my job now and focus on job hunting.
I'm a salaried, high-skilled worker. I intentionally chose not to share any more information for my own anonymity. For my anonymity, please do not share any more information even if you can infer it from this post.