Is it permissible to follow and disseminate morning dhikr that includes weak hadith, such as "Allah is sufficient for me; there is no god but He. In Him I put my trust, and He is the Lord of the Mighty Throne" seven times?

Working with a weak hadith concerning the virtues of deeds, such as adhkar (remembrance of Allah), is permissible under specific conditions. If it is permissible to act upon it, then it is permissible to disseminate it. The mentioned hadith, "Allah is sufficient for me; there is no god except Him. In Him I have placed my trust, and He is the Lord of the Mighty Throne," does not fall under the category of weak hadiths, as Sheikh Shu'ayb al-Arna'ut authenticated it.