Cell-free massive MIMO (CF-mMIMO) has emerged as a promising paradigm for delivering uniformly high-quality coverage in future wireless networks. To address the inherent challenges of precoding in such distributed systems, recent studies have explored the use of graph neural network (GNN)-based methods, using their powerful representation capabilities. However, these approaches have predominantly been trained and validated on synthetic datasets, leaving their generalizability to real-world propagation environments largely unverified. In this work, we initially pre-train the GNN using simulated channel state information (CSI) data, which incorporates standard propagation models and small-scale Rayleigh fading. Subsequently, we finetune the model on real-world CSI measurements collected from a physical testbed equipped with distributed access points (APs). To balance the retention of pre-trained features with adaptation to real-world conditions, we adopt a layer-freezing strategy during fine-tuning, wherein several GNN layers are frozen and only the later layers remain trainable. Numerical results demonstrate that the fine-tuned GNN significantly outperforms the pre-trained model, achieving an approximate 8.2 bits per channel use gain at 20 dB signal-to-noise ratio (SNR), corresponding to a 15.7 % improvement. These findings highlight the critical role of transfer learning and underscore the potential of GNN-based precoding techniques to effectively generalize from synthetic to real-world wireless environments.