normaly you should escape single quotes with two single quotes.
group.last_name like 'dsds''a'
will work in normal search so for stored query it should be something like
group.last_name like \'dsds\'\'a\'
in my test environment this does not work it does not load scoreboards at all, it seems that this is an CA bug, of course you can try to do this on your test system to see the results.
Alternatively you can use id of the group
group = U\'6706458ECED8FB4EA9E32EF5D10139E1\'