Praise be to Allah.
At-Tabaraani narrated in ad-Du‘aa’ (912):
Hafs ibn ‘Umar ibn as-Sabbaah ar-Raqqi told us: Khalaf ibn al-Waleed al-Jawhari told us: Abu Ja‘far ar-Raazi told us, from ‘Abd al-‘Azeez ibn ‘Umar ibn ‘Abd al-‘Azeez, from Saalih ibn Kaysaan, that ‘Ubaadah ibn as-Saamit (may Allah be pleased with him) said:
The Messenger of Allah (blessings and peace of Allah be upon him) used to teach us these words when Ramadan came, that one of us should say: “Allahumma sallimni min ramadan wa sallim ramadan li wa tasallimhu minni mutaqabbalan.”
The phrase “sallimni min ramadan” was narrated as “Allahumma sallimni li ramadan (O Allah, keep me safe until Ramadan),” as was recorded by adh-Dhahabi in Siyar A‘laam an-Nubala’ (19/51). Then adh-Dhahabi (may Allah have mercy on him) said:
It is ghareeb and was narrated only by Khalaf. End quote.
Abu Ja‘far ar-Raazi is ‘Eesa ibn Maahaan, concerning whom there were reservations about his accuracy and memory.
Adh-Dhahabi (may Allah have mercy on him) said:
Abu Ja‘far ar-Raazi is ‘Eesa ibn Maahaan.
Al-Jawzaqaani narrated from him via Salamah al-Abrash a marfoo‘ hadith from Qataadah, from al-Hasan, from al-Afnaf, from al-‘Abbaas: “If you let down a rope to the seventh earth…”
Then he said: Abu Ja‘far was one of those who were the sole narrators of munkar (odd) hadiths from famous narrators." Al-Mughni (2/777).
And he said:
Abu Ja‘far ar-Raazi at-Tameemi… Abu Zur‘ah said: He made many mistakes. an-Nasaa’i said: He is not strong, although Abu Haatim regarded him as thiqah (trustworthy)." (Al-Kaashif 2/416).
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said:
Abu Ja‘far ar-Raazi at-Tameemi…
He is sadooq (sincere), but with a poor memory." (Taqreeb at-Tahdheeb p. 629).
Saalih ibn Kaysaan did not meet ‘Ubaadah ibn as-Saamit.
At-Tirmidhi (may Allah have mercy on him) said:
Saalih ibn Kaysaan did not meet ‘Uqbah ibn ‘Aamir, but he did meet Ibn ‘Umar." (Sunan at-Tirmidhi 5/271).
‘Ubaadah died some time before ‘Uqbah (may Allah be pleased with them both).
It was narrated from al-Hasan al-Basri in a mursal report. It was narrated by Abu Bakr ash-Shaafa‘i in al-Ghaylaaniyyaat (185), where he said: ‘Abdullah told us: Zuhayr ibn Abi Zuhayr told us: Moosa ibn Ayyoob told us: Hammaad ibn Salamah told us, from Humayd, that al-Hasan said: When the month of Ramadan began, the Messenger of Allah (blessings and peace of Allah be upon him) used to say: “Allahumma sallimhu lana wa sallimhu minna.”
This is how this du‘aa’ was also narrated in a lengthy report narrated by Ibn Abi Dunya in Fadaa’il Ramadan (20), where he said: ‘Abd ar-Rahmaan ibn Waaqid told us: Damrah ibn Rabee‘ah told us: Bishr ibn Ishaaq told us, from Jaabir ibn Yazeed, that Abu Ja‘far said:
When the new moon was sighted for the month of Ramadan, the Prophet (blessings and peace of Allah be upon him) would turn to the people, then say: “O Allah, cause Ramadan to be for us a month of security, faith, safety, Islam, well-being, and relief from sickness, and help to fast, pray and recite Qur’an. O Allah, keep us safe until Ramadan and keep us safe for it and accept it from us so that before Ramadan departs You will have forgiven us, shown mercy to us and pardoned us…).
Its isnad includes Bishr ibn Ishaaq, from Jaabir ibn Yazeed; we could not find any biography for Bishr. It was narrated by Ibn ‘Asaakir with a different name, as he narrated in Taareekh Dimashq (51/186) from Damrah, from Bakr ibn Ishaaq, from Fayrooz, from Jaabir from Abu Ja‘far Muhammad ibn ‘Ali.
We do not know who Bakr ibn Ishaaq or Fayrooz are.
Jaabir ibn Yazeed is the one who narrated from Abu Ja‘far. They are two men, one of whom is weak, namely Jaabir al-Ju‘fi, and the other is sincere, namely Jaabir al-‘Ijli.
The isnad is also mursal.
In conclusion, this hadith does not have any saheeh (sound) isnad going back to the Prophet (blessings and peace of Allah be upon him).
But it was narrated from a number of the early generations that they used to recite a supplication similar to this. One example of that is what was narrated by at-Tabaraani with an isnad that appears to be hasan, from Makhool, as he narrated in ad-Du‘aa’ (913) from al-Haytham ibn Humayd: an-Nu‘maan ibn al-Mundhir told us, from Makhool, that he used to say when Ramadan began: “Allahumma sallimni li ramadan wa sallim ramadan li wa tasallamhu minni mutaqabbalan (O Allah, keep me safe until Ramadan, keep Ramadan safe for me, and accept it from me).”
For more information, please see the answer to question no. 37805 .
And Allah knows best.