diff --git a/inc/namespace.php b/inc/namespace.php
index bd505e1..c451dc4 100644
--- a/inc/namespace.php
+++ b/inc/namespace.php
@@ -304,8 +304,14 @@ function render_block_search( string $block_content, array $block, \WP_Block $in
 
 	$inherit = ! empty( $instance->context['query']['inherit'] );
 
+	// An inherited query is the main query, and WordPress resolves that from
+	// its own `s`: a term only reaches the search template because `s` is what
+	// routing reads. Naming the field anything else leaves the field blank on
+	// arrival, and clearing it deletes a parameter the URL never carried, so
+	// the results never change. `query-s` is still transposed onto the main
+	// query for anything that already links to it.
 	$query_var = $inherit
-		? 'query-s'
+		? 's'
 		: sprintf( 'query-%d-s', $instance->context['queryId'] ?? 0 );
 
 	// A search is a new set of results, so it belongs on the first page. Left
diff --git a/tests/e2e/README.md b/tests/e2e/README.md
index 83b3186..36ccf5b 100644
--- a/tests/e2e/README.md
+++ b/tests/e2e/README.md
@@ -34,7 +34,9 @@ run and `npm run playground:start`:
    deliberately private ones. It also records any PHP notice raised from this
    plugin's files and prints it into the page as a `qf-php-error:` comment,
    followed by a `qf-php-errors-checked` marker, so a spec can assert a page
-   rendered cleanly without depending on `display_errors`.
+   rendered cleanly without depending on `display_errors`, and rewrites the
+   theme's search results template to put a search block inside the inheriting
+   query loop, the one arrangement in which the blocks see an inherited query.
 5. Runs `tests/seed.php`, which creates the fixture terms, posts and the demo
    pages the specs visit.
 
diff --git a/tests/e2e/inherited-search.spec.js b/tests/e2e/inherited-search.spec.js
new file mode 100644
index 0000000..371d0b9
--- /dev/null
+++ b/tests/e2e/inherited-search.spec.js
@@ -0,0 +1,41 @@
+const { test, expect, POSTS } = require( './fixtures' );
+
+/**
+ * The search results template carries a query loop that inherits the main
+ * query, with a search block inside it — see tests/mu-plugins. A term reaches
+ * that page in WordPress' own `s`, because that is what routing reads, so the
+ * wired field has to be named `s` as well.
+ */
+test.describe( 'Search filter in an inherited query', () => {
+	test( 'the field is wired to the site search term', async ( {
+		page,
+		loop,
+	} ) => {
+		await page.goto( '/?s=Alpha' );
+
+		const input = page.locator( '.wp-block-query .wp-block-search__input' );
+		await expect( input ).toHaveAttribute( 'name', 's' );
+		await expect( input ).toHaveValue( 'Alpha' );
+
+		// The main query orders search results its own way, so compare as a set.
+		await expect
+			.poll( async () => ( await loop.titles() ).sort() )
+			.toEqual( POSTS.alpha );
+	} );
+
+	test( 'clearing the field clears the search', async ( { page, loop } ) => {
+		await page.goto( '/?s=Alpha' );
+		await expect
+			.poll( async () => ( await loop.titles() ).sort() )
+			.toEqual( POSTS.alpha );
+
+		await page
+			.locator( '.wp-block-query .wp-block-search__input' )
+			.fill( '' );
+
+		await page.waitForURL( /\?s=$/ );
+
+		// An empty term is still a search to WordPress, and returns everything.
+		await expect.poll( () => loop.titles() ).toContain( POSTS.beta[ 0 ] );
+	} );
+} );
diff --git a/tests/mu-plugins/register-test-content.php b/tests/mu-plugins/register-test-content.php
index caa8015..dee9572 100644
--- a/tests/mu-plugins/register-test-content.php
+++ b/tests/mu-plugins/register-test-content.php
@@ -12,6 +12,7 @@
 namespace HM\Query_Loop_Filter\Tests;
 
 add_action( 'init', __NAMESPACE__ . '\\register_test_content' );
+add_filter( 'get_block_templates', __NAMESPACE__ . '\\replace_search_template', 10, 2 );
 
 /**
  * Register the test post types and taxonomies.
@@ -100,3 +101,39 @@ function print_plugin_php_errors() : void {
 
 	echo "<!-- qf-php-errors-checked -->\n";
 }
+
+/**
+ * Put a searchable, inheriting query loop on the search results template.
+ *
+ * The bundled themes render search results through a query loop that inherits
+ * the main query, but none of them place a search block inside it. That is the
+ * arrangement a dedicated search page uses, and the only one where the filter
+ * blocks see an inherited query, so the tests need a template that has it.
+ *
+ * @param \WP_Block_Template[] $templates Templates matching the query.
+ * @param array               $query     Arguments the templates were queried with.
+ * @return \WP_Block_Template[] Templates, with the search template rewritten.
+ */
+function replace_search_template( array $templates, array $query ) : array {
+	if ( ! in_array( 'search', (array) ( $query['slug__in'] ?? [] ), true ) ) {
+		return $templates;
+	}
+
+	foreach ( $templates as $template ) {
+		if ( $template->slug !== 'search' ) {
+			continue;
+		}
+
+		$template->content = implode( '', [
+			'<!-- wp:query-title {"type":"search"} /-->',
+			'<!-- wp:query {"queryId":6,"query":{"perPage":10,"pages":0,"offset":0,"postType":"post","order":"asc","orderBy":"title","inherit":true}} -->',
+			'<div class="wp-block-query">',
+			'<!-- wp:search {"buttonText":"Search"} /-->',
+			'<!-- wp:post-template --><!-- wp:post-title /--><!-- /wp:post-template -->',
+			'</div>',
+			'<!-- /wp:query -->',
+		] );
+	}
+
+	return $templates;
+}