Complex sentence: She was sent south to the Falklands while conflict was still raging there, though by the time she was arriving the Argentineans had already surrendered, which allowed her to relieve her sister-ship "HMS Invincible".
Split into simpler sentences: She was sent south to the Falklands while conflict was still raging there. By the time she arrived the Argentineans had already surrendered and "Illustrious" relieved her sister-ship "HMS Invincible".