Thank you very much for the details, there is indeed an issue there. I'm not exactly sure why, but I suspect that the WPML table name might be incorrectly parsed by the search plugin, I'm not sure though. I'm guessing this, because on Multisites there might be a difference between the table prefix and the base table prefix variables.
Can you please add temporary FTP details as well? I would like to debug through the search code to see how the queries are executed, and why they fail. I should be able to fix it as well, if I can pinpoint the problem.Best,
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