Thanks jimzqui, you offered a fine solution to my problem, although I had to make few modifications to get the extra fields (created by Cimy User Extra Fields plugin) work properly:
1. Passing the user id
<input type=”hidden” name=”user_id” id=”user_id” value=”<?php echo $user_id; ?>” />
changed to
<input type=”hidden” name=”user_id” id=”user_id” value=”<?php echo $user_ID; ?>” />
2. Right names for extra fields
<td><textarea name=”RESUME” class=”mid2″ id=”resume” rows=”8″ cols=”50″><?php echo cimy_uef_sanitize_content($value); ?></textarea>
changed to
<td><textarea name=”cimy_uef_RESUME” class=”mid2″ id=”resume” rows=”8″ cols=”50″><?php echo cimy_uef_sanitize_content($value); ?></textarea>
3. Submit buttons
<p class=”CheckoutBtn”><?php _e(‘Update Profile »’, ‘cp’)?></p>
changed to
<input type=”submit” class=”button” value=”Update profile” name=”submit” />