I recently switched employers, and I'm waiting for an H1-B to be
approved. During this time, I got a much better job offer, we looked
for an immigration attorney to see if we could file for another H1-b
with the new company. He said we could file, and that I should stay
where I'm working now until we get either response, either my current
approval or the next. Now my employer says they'll file in two days,
but that I should give my current employer a notice right now, because
they'll be getting a letter from immigration saying that I'm running
another application... is this true? can't they just file? and once I
know the new process is in place I can quit my current job? This is a
very tough thing for me to do, I finally have a sponsor, steady job,
and even the new opportunity is great, can't they just wait to get the
acknowledgment for the new process?

so the question is? is it worth it for me to let my current employer
I'm leaving right now? should I do this now? or is it just a whim of
my new employer that I give the notice now so that they can have me
working with them asap?