Minor Correction

Title promotion does not matter to h1 as long as the job description does not change substantially.

But a promotion or change in job descriptions substantially during the pendency of a green card can jeopardize the green card process because the GC process is for a specific job, at a specific location, at a specific salary.

Of course, as I mentioned above, if you will come abck to work for your current position after you get the GC, you will be Ok not to do anything.