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Self-hosted site, want /cms subdir to point to webflow site, but keep URL from changing

I have a problem that I hope somebody can help out.

I have a self-hosted site. I want to use the CMS that is available through WebFlow, but from what I’ve read, to do that I will have host a site on

I would like to have a subdirectory off the self-hosted site called /cms that when you access it, it redirects to

I can already redirect through .htaccess or apache ProxyPass, but the URL changes to the webflow’s URL when you click on the link.

For SEO, is there any way to do what I’ve just described but keep the URL from changing to the WebFlow site? Is this even possible?