Spatiotemporal trajectory data is crucial for various applications. However, issues such as device malfunctions and network instability often cause sparse trajectories, leading to lost detailed movement information. Recovering the missing points in sparse trajectories to restore the detailed information is thus essential. Despite recent progress, several challenges remain. First, the lack of large-scale dense trajectory data makes it difficult to train a trajectory recovery model from scratch. Second, the varying spatiotemporal correlations in sparse trajectories make it hard to generalize recovery across different sampling intervals. Third, the lack of location information complicates the extraction of road conditions for missing points. To address these challenges, we propose a novel trajectory recovery model called PLMTrajRec. It leverages the scalability of a pre-trained language model (PLM) and can be fine-tuned with only a limited set of dense trajectories. To handle different sampling intervals in sparse trajectories, we first convert each trajectory's sampling interval and movement features into natural language representations, allowing the PLM to recognize its interval. We then introduce a trajectory encoder to unify trajectories of varying intervals into a single interval and capture their spatiotemporal relationships. To obtain road conditions for missing points, we propose an area flow-guided implicit trajectory prompt, which models road conditions by collecting traffic flows in each region. We also introduce a road condition passing mechanism that uses observed points' road conditions to infer those of the missing points. Experiments on two public trajectory datasets with three sampling intervals each demonstrate the effectiveness, scalability, and generalization ability of PLMTrajRec.