When using the List Filter Web Part to filter an external list your search will simply return the original list and is not filtered.
It is possible, however, to configure the List View Web Part to correct this problem.
To do this you need to edit the list List View Web Part settings. Click on Edit page.
Then Edit web part.
The select the Server Render option.
Then confirm the changes and you will be able to filter the list as normal.
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