Remove default filter from 'the_content' for the password reset page and add a new one to the login hook. This way the rest content of the page will not be lost.

wpmudev-ms-pass-reset-refilter.php

<?php
add_action( 'wp_head', function(){
	global $wp_filter, $post;

	if( ! class_exists( 'MS_Model_Pages' ) || $post->post_name != MS_Model_Pages::MS_PAGE_ACCOUNT || ! isset( $_GET['action'] ) || $_GET['action'] != 'rp' ){
		return;
	}
  
  // Originally uses the_content filter in MS_Controller_Frontend::user_account_manager()
  // Lets unset it so it displays the login's shortcode MS_View_Shortcode_Login::to_html()
  // So then we can hook in the ms_compact_code filter
	$hook = 'the_content';
  if( empty( $hook ) || !isset( $wp_filter[$hook] ) ){
    return;
  }

	foreach( $wp_filter[ $hook ] as $priority => $actions ) {
        foreach( $actions as $key => $data ) {
          //Looking for the 'MS_Controller_Frontend'
            if ( is_a( $data['function'][0], 'MS_Controller_Frontend' ) ) {
				//unset( $wp_filter[ $hook ][ $priority ][$key] );
                unset( $wp_filter[ $hook ][ $priority ] );
            }
        }
    }

}, 10 );

add_filter( 'ms_compact_code', function( $html, $data ){
	global $post;

	if( ! class_exists( 'MS_Model_Pages' ) || $post->post_name != MS_Model_Pages::MS_PAGE_ACCOUNT || ! isset( $_GET['action'] ) || $_GET['action'] != 'rp' ){
		return $html;
	}

	static $Reset_Result = null;

	if ( null === $Reset_Result ) {
		lib3()->array->equip_get( 'login', 'key' );
		lib3()->array->equip_post( 'pass1', 'pass2' );
		$rp_login = wp_unslash( $_GET['login'] );
		$rp_key = wp_unslash( $_GET['key'] );
		$err_msg = new WP_Error();
		$fatal_error = false;

		lib3()->array->strip_slashes( $_POST, 'pass1', 'pass2' );
		$pass1 = $_POST['pass1'];
		$pass2 = $_POST['pass2'];

		// Get the user object and validate the key.
		if ( $rp_login && $rp_key ) {
			$user = check_password_reset_key( $rp_key, $rp_login );
		} else {
			$user = false;
		}

		if ( ! $user || is_wp_error( $user ) ) {
			// If the user was not found then show an error message.
			if ( $user && 'expired_key' == $user->get_error_code() ) {
				$fatal_error = true;
				$err_msg->add(
					'password_expired_key',
					__( 'Sorry, this reset-key is not valid anymore. Please request a new reset email and try again.', 'membership2' )
				);
			} else {
				$fatal_error = true;
				$err_msg->add(
					'password_invalid_key',
					__( 'Sorry, we did not find a valid reset-key. Please request a new reset email and try again.', 'membership2' )
				);
			}
		} else {
			// If the user provided a new password, then check it now.
			if ( $pass1 && $pass1 != $pass2 ) {
				$pass1 = false;
				$err_msg->add(
					'password_reset_mismatch',
					__( 'The passwords do not match, try again.', 'membership2' )
				);
			}
		}

		if ( $fatal_error && count( $err_msg->errors ) ) {
			$url = esc_url_raw(
				add_query_arg(
					array( 'show' => 'lostpass' ),
					remove_query_arg( array( 'action', 'key', 'login' ) )
				)
			);

			$Reset_Result = sprintf(
				'[ms-note type="warning"]%s[/ms-note]<a href="%s">%s</a>',
				$err_msg->get_error_message(),
				$url,
				__( 'Request a new password-reset key', 'membership2' )
			);
		} elseif ( $pass1 ) {
			// This action is documented in wp-login.php
			do_action( 'validate_password_reset', $err_msg, $user );

			reset_password( $user, $_POST['pass1'] );

			// All done! Show success message and link to login form
			$url = esc_url_raw(
				remove_query_arg( array( 'action', 'key', 'login' ) )
			);

			$Reset_Result = sprintf(
				'[ms-note type="info"]%s[/ms-note]<a href="%s">%s</a>',
				__( 'Your Password has been reset.', 'membership2' ),
				$url,
				__( 'Login with your new password', 'membership2' )
			);
		} else {
			// This action is documented in wp-login.php
			do_action( 'validate_password_reset', $err_msg, $user );

			wp_enqueue_script( 'utils' );
			wp_enqueue_script( 'user-profile' );

			ob_start();
			if ( count( $err_msg->errors ) ) {
				printf(
					'[ms-note type="warning"]%s[/ms-note]',
					implode( '<br>', $err_msg->get_error_messages() )
				);
			}
			?>
			<form name="resetpassform" id="resetpassform"
				action="" method="post" autocomplete="off" class="ms-form">
				<input type="hidden" id="user_login"
					value="<?php echo esc_attr( $rp_login ); ?>" autocomplete="off"/>

				<p class="user-pass1-wrap">
					<label for="pass1"><?php _e( 'New password' ) ?></label><br />
					<div class="wp-pwd">
						<span class="password-input-wrapper">
							<input type="password" data-reveal="1" data-pw="<?php echo esc_attr( wp_generate_password( 16 ) ); ?>" name="pass1" id="pass1" class="input" size="20" value="" autocomplete="off" aria-describedby="pass-strength-result" />
						</span>
						<div id="pass-strength-result" class="hide-if-no-js" aria-live="polite"><?php _e( 'Strength indicator' ); ?></div>
					</div>
				</p>
				<p class="user-pass2-wrap">
					<label for="pass2"><?php _e( 'Confirm new password' ) ?></label><br />
					<input type="password" name="pass2" id="pass2" class="input" size="20" value="" autocomplete="off" />
				</p>

				<p class="description indicator-hint"><?php echo wp_get_password_hint(); ?></p>

				<br class="clear"/>

				<?php
				// This action is documented in wp-login.php
				do_action( 'resetpass_form', $user );
				?>
				<p class="submit">
					<input type="hidden" name="rp_key" value="<?php echo esc_attr( $rp_key ); ?>" />

					<button type="submit" name="wp-submit" id="wp-submit"
					class="button button-primary button-large">
					<?php _e( 'Reset Password', 'membership2' ); ?>
					</button>
				</p>
			</form>
			<?php
			$html = ob_get_clean();
			$Reset_Result = apply_filters( 'wpmudev_ms_compact_code', $html );
		}

		$Reset_Result = do_shortcode( $Reset_Result );
	}

	return $Reset_Result;
	
},10 , 2 );