Hello,
I occasionally do Wordpress web site transfers, and several of them were here on Freelancer.
If you check my profile you will see that I have perfect 5-star rating, and excellent employer reviews.
In order to do this transfer, I would need cPanel (to access database), FTP (to download/upload files) and Wordpress (to set new web site) admin access, for both old and new web site.
Best regards,
Nikola