You can make sure that the whole ticket thread is visible to the person you forward it to by enabling the 'Public ticket URL' option under Admin > Portals > Settings > Who can view tickets


Once this is enabled move to Admin > Email notifications > Templates > Forward Template and edit it so that the 'Public ticket URL' Placeholder is inserted to the Template. 


Once done, when clicking on 'Forward', the public ticket URL will be visible to the person who you forward it to and the whole ticket thread can be viewed by them.