Install it like a regular app
Because every tool runs locally in your browser with nothing uploaded, your device can keep a full offline copy of it, the same way it can with any other installed app. You'll only need a connection for the install itself.
Click the install icon (a screen with a down arrow) in the address bar, or open the browser menu and choose "Install PDkef".
Tap the Share button, scroll down, and select "Add to Home Screen".
Click the Share button in the toolbar and choose "Add to Dock...".
Your progress is never sitting in a browser tab alone
As you type into fields, tick checkboxes, or add a signature, the tool saves your progress to your device in the background. Close the tab, restart your computer, or lose power mid-form, and it's waiting for you exactly where you left it the next time you open the same file.
This is the same reason it can work offline in the first place: there was never a server in the loop to begin with, so there's nothing a lost connection can interrupt.