To what extent is the topic that includes forty benefits of praying upon the Prophet, peace and blessings be upon him, sound? Is it permissible to publish it in its entirety, or should what has not been authentically established or has been established by a weak hadith be omitted?

The mentioned benefits are taken from the book Jala' al-Afham by Ibn al-Qayyim, who is a relied-upon Imam. Therefore, there is no impediment to adopting and disseminating them. Reward is hoped for whoever disseminates them, as it encourages them to send prayers upon the Prophet, peace and blessings be upon him.