In Texas, a former employer, associate, client, or other entity with knowledge, can communicate with current or potential employers regarding a person's conduct or work history. However, if the entity says anything false with the intention of damaging that person’s business reputation or employability, that entity may be committing libel and slander. That entity may also be tortiously interfering with the person’s advantageous business relationships. If the entity’s false and malicious statements damage the person by preventing them from obtaining employment, or by causing them to be fired, that person may have a claim against the former employer.
If you feel your former employer's business associate is saying anything false about you and attempting to damage your reputation and/or prevent you from being hired, you should consult an employment attorney immediately. Be advised, however, that these cases are very difficult and it may be a challenge to find an attorney who will handle this on a contingency agreement.
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Are you putting this other entity on applications or your resume as a referral? Removing that company as a referral would likely be your easiest course of action.
You may have some options available to pursue this other company but it depends significantly on what is being said and whether it is untrue as a statement of fact or merely an opinion that you disagree with.