Is one allowed to write texts/send messages in the name of another person, who has given his permission for this?
Concrete example: Jack (a boss of a company) hires a marketing firm to go into his (personal) LinkedIn account, and the marketing firm will send (in Jack’s name) messages to potential customers to buy his (Jack’s) products or services.
The marketing company will send a message (in Jack’s name and from Jack’s account) to John (a potential customer) asking him (John) to buy the product/service. John thinks Jack is sending him this message, and decides to buy the product (because he likes that Jack personally contacted him, for example).
Is this allowed according to halacha or not? If so, what can be done to make it allowed? (Does Jack have to put in his LinkedIn bio that this is a business account managed by his marketing team, for example?)