Is it permissible to repeat the supplication "O Allah, help me to remember You, to give thanks to You, and to worship You well" before and after the salaam, based on the differing opinions of scholars regarding its proper place?

"End of the prayer" can mean either the very end of the prayer or after it. The hadith (definition) uses wording that indicates "end of the prayer" refers to a point within it, before exiting it, such as: "Do not neglect to say in every prayer," and "Say them in every prayer." Al-Buhuti and Ibn Taymiyyah mentioned it among the supplications to be recited after the Tashahhud (definition) and before the Tasleem. It has not been reported that the worshipper should say this supplication twice, so one should confine oneself to one of the two positions. A Muslim should act according to what they deem most probable or emulate a scholar they trust.