Her GC was approved for "staff member" position. So DOL recognized lack of available workers in this position and certified LC for this position. Then USCIS verified that your wife had had the proper background to take this position and considered a letter of employment from her employer, that indicated the intention of the employer to employ your wife as a "staff member" as soon as GC would be approved.
Then USCIS approved your wife's GC based on all the assumptions and cosiderations above. And now, one month later, you wife changes the position from "staff member" (approved by DOL/CIS) to "manager" which might have enough work force in the US already.
Well, even though your wife is changing the job within the same company, it might hurt her when she applies for citizenship, since this is a direct violation on INA. Well, I am saying "might" not "will". It'll depend on how tolerant the USCIS officers will be to such situations at the time, when your wife files N-400
Remember! Your GC is approved for the specific position in the specific company. It's not like "any position in the specific company" or "the specific position in any company". I don't want to say that such a quick promotion will cause issues, but it still might. So, consider the risks and make your own decision.