Duration between H-1B ammendment and h-1b transfer to new company?

Question

hello,

 

I  changed my job title/discription within same company-A and my lawyer wants to file H-1b ammendment for this.

But i  am also looking for a new job outside. Assuming I get a job in next month, I may have to do an H-1b transfer to the new company. In this case, what should I do if my H-1B ammendment and H-1B tranfer application overlaps or are processed very close to each-other?

Is there a rule specified for minimum duration between H-1B ammendment (with company -A) and new H-1 transfer (for company B)?

What if they overlap at USCIS?

I am thinking, may be I will file H-1B ammendment on priority and get it done in next 3 weeks and then can start my H-1B transfer application? Is this the safe option, filing H-1B ammendment and then new H-1B within a month's time?

Please let me know your suggestions.

 

thanks,

SL