"To continue the investigation" means to keep gathering information and examining evidence in order to uncover more facts or find answers to unresolved questions. Full definition
Military police will continue their investigation into exactly when the combat and training item disappeared. (wrvo.org)
The researchers are analyzing more patient samples looking for additional cases of multiple copy number variants to continue their investigation of what may trigger this rare phenomenon. (sciencedaily.com)
It allows you to play through part of Chapter 1, and then transfer your progress to the full game if you're interested in continuing your investigation! (perfectly-nintendo.com)