Praise be to Allah.
This hadeeth (narration) has no basis in the books of Sunnah (prophetic teachings). It would appear to be one of the fabricated hadeeths that speak of the virtues of praying in Sha‘ban. A number of hadeeths were fabricated and falsely attributed to the Messenger (peace and blessings be upon him) about the virtues of Sha‘ban and pray during this month, and the night of the fifteenth of the month. Al-‘Allamah Ibn Hajar al-Haytami (may Allah have mercy on him) said: All the hadeeths which speak of the virtues of this night – meaning the night of the first Friday of Rajab and the night of the fifteenth of Sha‘ban – are false and have no basis, even though they appear in some books by major scholars such as al-Ghazali’s Ihya ‘Uloom ad-Deen and so on. End quote.
Al-Fatawa al-Fiqhiyyah al-Kubra, 1/184
Similarly, hadeeths were fabricated about the virtue of praying on certain days of the week.
Ash-Shawkani (may Allah have mercy on him) said: With regard to what is said about praying on Sunday, Monday or other days of the week, there is no dispute among the scholars of hadeeth that these are fabricated hadeeths and that this prayer is not regarded as mustahabb (recommended) by any of the leading scholars. End quote.
Al-Fawaid al-Mawdoo‘iyyah, 1/74
So it is not permissible to act upon this false and fabricated hadeeth. The saheeh (authentic) hadeeths are sufficient for the one who wants to truly follow the Prophet (peace and blessings of Allah be upon him).
And Allah knows best.