make sure your redirect is ALWAYS a single redirect not a chain.
so lets your new site is: https:// www.test{dot}com
then what you want is:
http:// test{dot}com -> https:// www.test{dot}com
http:// www.test{dot}com -> https:// www.test{dot}com
https:// test{dot}com -> https:// www.test{dot}com
and not for example
http:// test{dot}com -> http:// www.test{dot}com -> https:// www.test{dot}com
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