i agree with Justfunny only if you want to apply for citizenship in future. In another words, it does not really matter when you change the job if you plan not to get the US citizenship. But if you plan to change your green card ultimately to the citizenship then it is better option to stay with the company A for at least one year. My cousin was asked to show the proof of the employment with the company in the citizenship interview. From what I know, there is chance of you being asked that question in the citizenship interview and as well as of not being raised that question to you. Its matter of luck. If that paper is being asked and you cannot provide that paper then you are ineligible for the process and you will be deported for not abiding with the US laws.