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I have a simialr problem... In December, a client site switches from http to https. Any clicks from old backlinks redirect from the http target to https, so the traffic still flows. But because the backlinks are to http, not https, the latter version has lost the Domain Authority. How do we resolve this? Is the only solution to approach referring sites and ask them to change links to https?

Duplicate content isn't a big deal for ecommerce sites, you're unlikely to be penalized for it.