Another messenger is offered by Facebook: Facebook Messenger. On the one hand, it is possible, of course, to send Facebook messages to other people and pages using Facebook's desktop version. On the other hand, Facebook Messenger offers a new smartphone app because the Facebook app no longer allows sending direct Messages.
In general, you should allow or enable users to send messages to your page and not disable this function.
Under "Settings" of the Facebook page, you can choose further options for sending messages to the page.
The "Response Assistant" is particularly interesting. You can define automated answers for different scenarios.
The Response Assistant can be configured for the following cases:
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