how long do we need to stick with current employer after GC approval ?

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Usually people stay as per the agreement they may have signed for their company to sponsor green card. You can leave the next day. As far as I know INS does not have a clear rule on this. Some of these web sites say that if you leave try to find a similar job but then again I have not heard that any one got in trouble with the INS for leaving a job that got him/her the green card.
 
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"Technically" forever (that was your intent for GC in the first place). Now to classify "technically" ... your interpretation is as good as ours.
 
If you are going to apply for Citizenship later..check this out

As long as you intend to stay in GC status you should be OK. If you are applying for Citizenship then they look at your GC process and if you have quit the company that has sponsored your GC within 6 months of getting GC you might have to explain the situation to INS. This is the advice I got from a friend who went through the same situation- who is not a legal expert. Check this out before u make any decision.
 
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stick to same company for at least 6 months maybe more
evaluate the risk of changing jobs very carefully and change only if there is a big improvement in job (but not before 6 months)
 
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