"I moved from Alberta to Ontario in July 2018 to look for a new job. Unfortunately I have not been able to find one and have been collecting unemployment insurance. Can I claim the moving expenses against EI funds received?
No, you can only claim Moving Expenses against income "earned" at the new location, and EI does not qualify as earned income.
CRA can disallow a moving expense claim if you didn't specifically move to go to school or for a new job. They consider a move to look for a better job to be personal and therefore the moving expense deduction is not valid.