Can't figure it out why you are using $person["Fs"] inside input tag
May be this should help
echo (isset($person['Fs']) ? '</br><input type="checkbox" name="inputFs" value="1"/>Syns på förstasidan' : '');
OR
If you are using $person["Fs"] for value then try this
echo (isset($person['Fs']) ? '</br><input type="checkbox" name="inputFs" value="' . $person["Fs"] .'"/>Syns på förstasidan' : '');
If your checking for a variable if it is blank or contain some particular value.
Then you don't have to use isset it works without isset
Consider your checking if $person['Fs'] == "checked" then use
echo ($person['Fs'] == "checked" ? '</br><input type="checkbox" name="inputFs" value="' . $person["Fs"] .'"/>Syns på förstasidan' : '');