I made a Memrise card template for Anki, which makes reviewing in Anki work very much like the classic review in the current version of the site:
The card version avoids layout bugs, such as jumping text on answer submission and cropped fonts,
present in the original design:
Here is an interactive demo of the card template to see how it works without downloading anything.
The template is intended to be a supplement for the courses exported from Memrise (but can be used in other ways, of course).
Right now it lacks audio buttons and some other minor features, but they can be added if requested. I can also add some retired functionality from the previous versions of the site, such as timer and Mems.
The card template can be downloaded directly from AnkiWeb or from its GitHub page, which can also be used for reporting issues.
In case you have any questions regarding using the template or need help customizing it for your own use case, leave a comment here, and I will be happy to help.
In case this forum stops working again here is the Anki forum thread to continue the discussion.