Complex sentence: After obtaining full control of the international licensing outside of the United States, Lyons and its successors handled global franchising through their UK-based subsidiary Wimpy International Ltd. until Wimpy UK became a subsidiary of South Africa-based Famous Brands in 2007.
Split into simpler sentences: After obtaining full control of the international licensing outside of the United States, Lyons and its successors handled global franchising through their United Kingdom based subsidiary "Wimpy International Ltd". This was until Wimpy UK became a subsidiary of South Africa based Famous Brands in 2007.