Speech brain-computer interfaces (BCIs) aim to restore communication for people with paralysis by translating neural activity into text. Most systems use cascaded frameworks that decode phonemes before assembling sentences with an n-gram language model (LM), preventing joint optimization of all stages simultaneously. Here, we introduce an end-to-end BraIn-to-Text (BIT) framework that translates neural activity into coherent sentences using a single differentiable neural network. Central to our approach is a cross-task, cross-species pretrained neural encoder, whose representations transfer to both attempted and imagined speech. In a cascaded setting with an n-gram LM, the pretrained encoder establishes a new state-of-the-art (SOTA) on the Brain-to-Text '24 and '25 benchmarks. Integrated end-to-end with audio large language models (LLMs) and trained with contrastive learning for cross-modal alignment, BIT reduces the word error rate (WER) of the prior end-to-end method from 24.69% to 10.22%. Notably, we find that small-scale audio LLMs markedly improve end-to-end decoding. Beyond record-setting performance, BIT aligns attempted and imagined speech embeddings to enable cross-task generalization. Altogether, our approach advances the integration of large, diverse neural datasets, paving the way for an end-to-end decoding framework that supports seamless, differentiable optimization.