Apologies. The freezing is about the buddydev.com page.

The theme I use on the site is the Community Builder Pro Child and the template pack is the “legacy”.
The code I have used is shown below.

/**
 * Get a link to send a BetterMessage PM to the given User.
 *
 * @param int $user_id user id.
 *
 * @return string
 */
function bm_get_send_private_message_to_user_url( $user_id ) {
    return bp_loggedin_user_domain() . 'bp-messages/?new-message&fast=1&to=' . bp_core_get_username( $user_id );
}
/********************
//Show private message button on members list
********************/
/**
 * Get the User Id in the current context
 * @param int $user_id
 * @return int user_id
 */
function hibuddy_get_context_user_id($user_id=false){

if ( bp_is_my_profile() || !is_user_logged_in() )
 return false;
 if( !$user_id )
 $user_id = bp_get_member_user_id();//for members loop
 if( !$user_id && bp_is_user() ) //for user profile
   return false;
 //$user_id = bp_displayed_user_id();

 return apply_filters( 'hibuddy_get_context_user_id', $user_id );
}

function hibuddy_get_send_private_message_button() {
	// get the user id to whom we are sending the message
	$user_id = hibuddy_get_context_user_id();	

	if (!$user_id || $user_id == bp_loggedin_user_id())
		return;
	$defaults = array (
	'id' => 'private_message-'.$user_id,
	'component' => 'messages',
	'must_be_logged_in' => true,
	'block_self' => true,
	'wrapper_id' => 'send-private-message-'.$user_id,
	'wrapper_class' => 'send-private-message',	
	'link_href' => bm_get_send_private_message_to_user_url($user_id),
	'link_title' => __('Send a private message to this user.', 'buddypress'),
	'link_rel' => __('Private Message', 'buddypress'),
	'link_class' => 'send-message'
	);

	$btn = bp_get_button( $defaults );

	return apply_filters('hibuddy_get_send_private_message_button', $btn);
}

function hibuddy_send_private_message_button() {
  $user_id = hibuddy_get_context_user_id();
  //echo buddydev_private_message_button_shortcode( $user_id );
  echo hibuddy_get_send_private_message_button();
}

if ( bp_is_active( 'messages' ) ){
	add_action( 'bp_directory_members_actions', 'hibuddy_send_private_message_button', 10 );
  	//experiment with the last value to change position
}

Thank you, for your help Brajesh.

Along with the change in function below (Removed the bp_is_my_profile() check), did the trick!

function hibuddy_get_context_user_id($user_id=false){

if ( !is_user_logged_in() )
 return false;
 if( !$user_id )
 $user_id = bp_get_member_user_id();//for members loop
 if( !$user_id && bp_is_user() ) //for user profile
   return false;
 //$user_id = bp_displayed_user_id();

 return apply_filters( 'hibuddy_get_context_user_id', $user_id );
}

Regards,
Sotiris