Inspired by the \emph{Well-initialized Lottery Ticket Hypothesis (WLTH)}, we introduce Soft-Transformer (Soft-TF), a parameter-efficient framework for continual learning that leverages soft, real-valued subnetworks over a frozen pre-trained Transformer. Instead of relying on manually designed prompts or adapters, Soft-TF learns task-specific multiplicative masks applied to the key, query, value, and output projections in self-attention. These masks enable smooth and stable task adaptation while preserving shared representations. Combined with a lightweight dual-prompt mechanism, Soft-TF maintains strong knowledge retention and mitigates Catastrophic Forgetting (CF). Across multiple continual learning benchmarks, Soft-TF achieves state-of-the-art performance, consistently outperforming prompt-based, adapter-based, and LoRA-style baselines while requiring minimal additional parameters.