This paper addresses the problem of accelerating the construction of accurate editorial annotations for handwritten archival texts within an incremental training cycle based on weak transcription. Unlike our previously published results, the present work focuses on integrating automatic post-correction of weak transcriptions using large language models (LLMs). We propose and implement a protocol for applying LLMs at the line level in a few-shot setup with carefully designed prompts and strict output format control (preservation of pre-reform orthography, protection of proper names and numerals, prohibition of structural changes to lines). Experiments are conducted on the corpus of diaries by A.V. Sukhovo-Kobylin. As the base recognition model, we use the line-level variant of the Vertical Attention Network (VAN). Results show that LLM post-correction–exemplified by the ChatGPT-4o service–substantially improves the readability of weak transcriptions and significantly reduces the word error rate (in our experiments by about −12 percentage points), without degrading the character error rate. Another service tested, DeepSeek-R1, demonstrated less stable behavior. We discuss practical prompt engineering, limitations (context length limits, risk of “hallucinations”), and provide recommendations for the safe integration of LLM post-correction into an iterative annotation pipeline to reduce expert annotators’ workload and speed up the digitization of historical archives.