Start here - https://moz.com/blog/seo-guide-how-to-properly-move-domains

Start there and then read hundreds of other snakeoil tutorials and in the end you still wont know what the correct way is.

Any relatively experience Technical SEO will know how to do this its not rocket science you just have to pay detail attention to the site.

Unfortunately a lot of ecommerce sites are of low quality and coded by the finance directors golfing mates "friends" company.