No direct trading between Game Boy Advance (GBA) and Nintendo DS/DS Lite. They use different hardware link protocols (Serial vs. Wireless) and save structures.
Use homebrew on 3DS (CFW + Checkpoint/JKSM) to extract GBA saves from cart/VC, convert to .pk3/.pk4/.pk5, inject into HOME. Requires technical skill.
Bottom Line: No cable connects GBA ↔ DS for trading. One-way migration via Pal Park (DS/DS Lite only) is the official path.