I do not see how anyone could FORCE you company to train another. It sounds like your company may have consulted their insurance carrier. Of course, your company MAY train others - there are companies in the full time business of training. But, your company appears to have made a valid decision. Discuss with an attorney, if need be. You can find a local attorney.
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I agree with Attorney Poulson, your employer can not be forced (absent some contractual obligation) to train the new company's employees, but (to minimize the loss of business) it may enter into an agreement to do so for consideration.
I suppose it is possible that if there is overlap in the contract of both companies and there is a contractual provision in the contract of your current employer that permitted your client to direct work the work that is performed that some obligation is created, but that would be highly fact specific.
I would suggest that your current employer take the existing contract to an attorney and seek advice.
I am licensed in New Mexico and Pennsylvania, and therefore any discussion of issues related to other states must considered within that context. In addition, my comments are not intended to create a legal representation but merely to respond to the limited facts presented by the question. Any opinion herein is not meant as a precise statement of legal rights or as a recommendation of any particular course of action. A more complete legal review can be obtained through local counsel.
I'm wondering if the client's request for "training" of the new staff was really that - or more in the nature of a request that the first company's staff (your company) provide information to the new staff (the other company) about what's been done in the past / past problems or issues. This type of "hand-off" is routinely done between health care providers - whether they work for the same company or not.
But - you should follow the direction you are given by your supervisor. Your employer gets to set the limits on what they will pay you to do.
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