What is the ruling on messages that make the recipient swear to resend them to others, such as messages to "send prayers upon the Prophet" that warn against stopping the campaign or missing out on a billion good deeds?

Sending good messages is permissible, and the recipient is not obligated to send them to others. Whoever sends them will be rewarded, Allah willing, and there is no sin upon whoever does not send them. It is stipulated that these messages contain what is legislated by the Sharia.