Moving expense, transferred to Quebec. Renting in BC, bought home in Quebec in April, closed sale in July. Moved in June to Quebec . Notary fee, tax on home expense?

You were renting and living in BC then moved to QC and purchased a house. So yes, you can definitely claim your moving expenses. You will also claim the purchase of a new home. TurboTax has great articles to assist  you on what you can claim. 

Moving Tax Deductions in Canada

How to Claim Moving & Relocation Expenses in Canada

Where do I claim the home buyers' amount?

Thank you for choosing TurboTax.