Intracranial electrocorticography (ECoG) offers high-signal-to-noise access to cortical activity for brain-computer interfaces, yet limited per-patient data has led most prior work to rely on small, subject-specific decoders that neglect information shared across patients. We investigate whether large pretrained scalp-EEG foundation models (EEG FMs) can be adapted to ECoG, enabling cross-patient learning and competitive decoding performance while calibrating to a held-out patient in 10-30 minutes on a single GPU. We introduce CORTEG, a cross-modality transfer framework that combines a pretrained EEG FM backbone, an electrode-aware KNNSoftFourier spatial adapter, a dual-stream tokenizer for low-frequency and high-gamma activity, and a leave-one-subject-out fine-tuning strategy. We evaluate CORTEG on two challenging regression tasks: public finger trajectory regression (n=9) and private audio envelope regression (n=16). CORTEG matches or exceeds the strongest task-specific baselines on both tasks: it reaches the highest mean correlation among compared methods on the public finger benchmark (gain not statistically significant on n=9 subjects), with larger and statistically significant gains on the audio task and in low-data per-patient calibration. Feature analyses align with neurophysiology, and latent manifolds capture low-dimensional finger-movement structure. CORTEG provides systematic evidence that scalp-EEG pretraining can be repurposed for ECoG decoding, enabling data-efficient intracranial BCIs that can adapt to new patients.