To see how a parent can setup a Scout to participate in Scoutbook, see the instructions towards the bottom of the page, here: https://help.scoutbook.scouting.org/knowledge-base/scoutbook-tutorial-for-parents/
There are some issues that typically occur when the parents are unable to invite their Scout to Scoutbook.
1. The Scout has previously been invited and accepted. To see if this is the case, go to Send Message for the unit. If the Scout’s name appears in the Scout field, an invitation has been sent and accepted. To find out the user ID associated with the Scout, send a test message to the Scout, copy yourself and make sure BCC is turned off. This will reveal the Scout’s e-mail address in your copy of the e-mail.
2. Only a parent can invite a Scout to Scoutbook. The Parent/Guardian check box must be set on the parent’s connection to the Scout. You will need to reset the parent connections to the Scouts by clicking on the Scout > Scout’s Connections > Select the parent’s name > Check the Parent/Guardian box > Update.
3. There are some instances where the parent/Scout relationship is not set properly internal to Scoutbook. To fix this, a unit admin first edits the parent/Scout connection to turn on the Adult Leader connection type (if it is not already on) then have the parent turn off the Parent/Guardian check box and save the connection. They can then edit the connection again and turn the Parent/Guardian check box back on. Finally, the Adult Leader connection type needs to be cleared (if it was not initially on). This should then allow the parent to invite the Scout.
4. If the Invite Scout option is not visible to the parent in the Edit Extended Information page, the parent should check for an email in the Scout’s profile page. If there is an email there, then the Scout may be able to login to http://my.scouting.org and reset their password. Or create an account then login to Scoutbook. See the video below starting at 1:40
5. Finally, if all else fails, reach out on the forums for assistance: https://discussions.scouting.org/