We need to replace existing string 120:
$output .= '<div>'. l('more', 'user_activity') .'</div>';

by new one:
$output .= theme_more_link('/user_activity', t('Activity'));

"more" link in the block will be be translated correctly.

Comments

Ivan Simonov’s picture

Ivan Simonov commented

also string 'User activity' conflicts with existing one and have different interpretations

 User activity
modules/user/user.module:721

Suggest to change 'User activity' string to 'Users activity'
It help to avoid conflicts and translate it correctly.