Talk to Mechanic to get a hacking device

Hand the fragment to Mechanic and he'll either mail you the Local network hacking device directly (free, but takes some time to arrive in messages) or offer a barter. Wait for the mail if you can — saves materials. The hacking device is the thing you'll plant inside The Lab next step. Don't sell or trade it; it's a quest item but accidentally barter-clicking can void it. Move it straight into your stash and leave it there until you queue Lab.