As mentioned by Esra, you can do that but it will be a policy violation, so it is better to avoid, however, one thing you can do is, you can send them to your store and have your other brand products linked there, to move the traffic, you can do this on your own risk.
No, it is recommended that do not send any type of link to customer in the messaging because amazon does not support this and it is also against the amazon’s polices.
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