Nowadays, false and unverified information on social media sway individuals' perceptions during major geo-political events and threaten the quality of the whole digital information ecosystem. Since the Russian invasion of Ukraine, several fact-checking organizations have been actively involved in verifying stories related to the conflict that circulated online. In this paper, we leverage a public repository of fact-checked claims to build a methodological framework for automatically identifying false and unsubstantiated claims spreading on Twitter in February 2022. Our framework consists of two sequential models: First, the claim detection model identifies whether tweets incorporate a (false) claim among those considered in our collection. Then, the claim retrieval model matches the tweets with fact-checked information by ranking verified claims according to their relevance with the input tweet. Both models are based on pre-trained language models and fine-tuned to perform a text classification task and an information retrieval task, respectively. In particular, to validate the effectiveness of our methodology, we consider 83 verified false claims that spread on Twitter during the first week of the invasion, and manually annotate 5,872 tweets according to the claim(s) they report. Our experiments show that our proposed methodology outperforms standard baselines for both claim detection and claim retrieval. Overall, our results highlight how social media providers could effectively leverage semi-automated approaches to identify, track, and eventually moderate false information that spreads on their platforms.