Index: src/js/_enqueues/admin/privacy-tools.js
===================================================================
--- src/js/_enqueues/admin/privacy-tools.js	(revision 45539)
+++ src/js/_enqueues/admin/privacy-tools.js	(working copy)
@@ -71,7 +71,13 @@
 		clearResultsAfterRow( $requestRow );
 
 		function onExportDoneSuccess( zipUrl ) {
-			setActionState( $action, 'export-personal-data-success' );
+			var summaryMessage = strings.emailSent;
+
+			setActionState( $action, 'export-personal-data-idle' );
+
+			appendResultsAfterRow( $requestRow, 'notice-success', summaryMessage, [] );
+			$this.hide();
+			
 			if ( 'undefined' !== typeof zipUrl ) {
 				window.location = zipUrl;
 			} else if ( ! sendAsEmail ) {
@@ -168,7 +174,8 @@
 					classes = 'notice-warning';
 				}
 			}
-			appendResultsAfterRow( $requestRow, 'notice-success', summaryMessage, messages );
+			appendResultsAfterRow( $requestRow, classes, summaryMessage, messages );
+			$this.hide();
 		}
 
 		function onErasureFailure() {
Index: src/wp-admin/includes/class-wp-privacy-data-export-requests-list-table.php
===================================================================
--- src/wp-admin/includes/class-wp-privacy-data-export-requests-list-table.php	(revision 45539)
+++ src/wp-admin/includes/class-wp-privacy-data-export-requests-list-table.php	(working copy)
@@ -101,7 +101,6 @@
 				?>
 				<span class="export-personal-data-idle"><button type="button" class="button export-personal-data-handle"><?php _e( 'Send Export Link' ); ?></button></span>
 				<span class="export-personal-data-processing button updating-message hidden"><?php _e( 'Sending Email...' ); ?></span>
-				<span class="export-personal-data-success success-message hidden"><?php _e( 'Email sent.' ); ?></span>
 				<span class="export-personal-data-failed hidden"><?php _e( 'Email could not be sent.' ); ?> <button type="button" class="button export-personal-data-handle"><?php _e( 'Retry' ); ?></button></span>
 				<?php
 
Index: src/wp-includes/script-loader.php
===================================================================
--- src/wp-includes/script-loader.php	(revision 45539)
+++ src/wp-includes/script-loader.php	(working copy)
@@ -1691,6 +1691,7 @@
 				'noneRemoved'     => __( 'Personal data was found for this user but was not erased.' ),
 				'someNotRemoved'  => __( 'Personal data was found for this user but some of the personal data found was not erased.' ),
 				'removalError'    => __( 'An error occurred while attempting to find and erase personal data.' ),
+				'emailSent'       => __( 'Email sent.' ),
 				'noExportFile'    => __( 'No personal data export file was generated.' ),
 				'exportError'     => __( 'An error occurred while attempting to export personal data.' ),
 			)