Assalaamu alaykum wa rahmatullaahi wa barakaatuhu, Shaykh. It was reported by At-Tabarani that the Prophet, sallallaahu 'alayhi wa sallam, said, “The one who recites Ayat-ul-Kursi after the conclusion of an obligatory prayer is under the Care of Allaah until the next prayer commences.” [At Targheeb wat-Tarheeb (2:435)] I read this hadith and would like to know its authenticity. May Allaah reward you, Shaykh.
All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
The hadeeth with the wording that you mentioned was classified as good by Al-Munthiri in At-Targheeb and by Al-Haythami in Al-Majma’. However, some other scholars classified it as weak; for instance, Ibn Hajar said in Nataa'ij Al-Afkaar, “This is a strange hadeeth, and its chains of narrators is weak.”
This hadeeth was also classified by Al-Albaani as weak in As-Silsilah Adh-Dha’eefah because one of its narrators, Hafs ibn Umar ar-Raqaashi, is unknown.
Nevertheless, there is an authentic hadeeth with the following wording: “Whoever recites Aayat-ul-Kursi [Quran 2:255] after each obligatory prayer, then nothing prevents him from entering Paradise except death.” [An-Nasaa’i and Ibn Hibbaan graded it saheeh (sound) and so did Al-Albaani]
Allah knows best.
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