Shaykh Abdul Haq Muhaddith Dehlawi quotes this Hadith in his famous "Ma Thabata Minas Sunnah" As narrated by Imam Hasan Basri, Mursal riwaayat above fact should suffice as proof that Hadith is not fabricated.
The Revered and Renowned Prophet - Peace and Blessings be upon him - said: Rajab is the month of Allah, Sha’bān is my month, and Ramadan is the month of my Ummaĥ. (Al-Firdaus bimā Šaur-ul-Khattāb, vol. 2, pp. 275, Hadīš 3276) http://www.dawateislami.net/bookslibrary/104 RETURN OF THE SHROUD page 9/10 I found the above reference will let you know if there is information about the grading. not directly related to above but useful info on grading: http://www.alahazrat.net/islam/what-is-daeef-hadith-how-it-becomes-hasan.php https://musjidulhaq.com/2015/07/30/a-summary-of-hadeeth-sciences/ In conclusion I would like to mention that grading is relevant in matters concerning rulings in Fiqh and matters of Aqaid. For example to reject those beliefs established upon MUTAWATTIR Hadith ( highest grading) would be KUFR whilst not accepting matters established upon Hadith upon which the grading of the ISNAD is DAEEF would not hold the same HUKM. Likewise the FOUR IMAAMS of Fiqh had also established what is FARD, WAJI,SUNNAH and HARAAM upon the different levels of grading and their IJTIHAD on matters. If we are not trying to prove something as a matter of ESSENTIAL AQAID or we are not trying prove any rulings as an essential part of our fiqh meaning FARD, WAJIB ,SUNNAH or HARAAM , I do not see the need to make an issue of the grading if we are merely encouraging good.
What's the grading of the hadith: Rajab is the month of Allah, Sha'ban is my month and Ramadan is the month of my ummah.