Text-based sequential recommender systems, while greatly improving recommendation accuracy by incorporating item contexts, are undeniably more expensive to train. By condensing a large dataset into a compact set of synthetic samples for model training, dataset distillation offers a promising solution. However, its adoption in text-based sequential recommendation is non-trivial given the large pool of discrete items. This challenge is further compounded by language model-based item encoding, which makes bi-level optimization commonly used in dataset distillation prohibitively expensive. To this end, we propose First-order dataset distillation for Text-based Sequential Recommendation (FOSTER), which facilitates effectiveness and efficiency via three novel components: (1) stochastic item subset sampling that replaces costly full-corpus embedding extraction at each distillation step; (2) first-order optimization with trajectory-anchored parameter reset to avoid expensive bi-level gradient computation; and (3) regularization that explicitly promotes co-occurrence between semantically similar items in the synthetic sequences. Extensive experiments on three benchmarks show that FOSTER consistently outperforms existing dataset distillation and coreset selection baselines, approximating full-dataset performance using as few as 20 synthetic interaction sequences.