From muthy.com.
Under pre-AC21 law, a person had to work for the sponsoring employer for a reasonable time after receiving the "green card" to avoid any potential future findings of fraud or misrepresentation. A reasonable time is a fact-specific matter, but many attorneys recommend a minimum of six months and preferably a year or longer. Therefore, it is best to make it clear exactly which employment offer formed the basis of the I-485 approval. In some cases, the BCIS may approve the I-485 either before receiving the information on the change in employers or before their mailroom processes that information. It is best to notify them upon switching employers so that the BCIS records will reflect their having received the appropriate documentation when the person files for citizenship.
Failure to notify the BCIS of a change in employer may, at the very least, cause confusion in the future if the case is ever reviewed. In other instances, it may be deemed as fraudulent not to notify the BCIS. This review could happen if the person has any inappropriate immigration or criminal involvement. For law-abiding individuals, the case will be reviewed if the person seeks to naturalize to U.S. citizenship. In order to naturalize, the green card must be obtained in a legitimate manner. For employment-based green cards, the length of employment with the sponsor following green card approval is important in the BCIS determination of whether the approval was properly issued. We still do not know how AC21 has modified the pre-AC21 law in this regard but it makes sense that there must be some leeway.