回复：H1b approval transfer - 863211 question again

You can ask your new employer to file a new h1 petition for you, not h1 tranfer because your status is not h1 yet. But you do not need a new quote if your current employer does not cancel the h1. Also, there are still many H1 quote available, so just ask your new employer to file a new h1 application as soon as possible so that you do not need to worry about whether your current employer will cancel the H1 or not.