Hello Vasily,
Thanks for writing in!
To resolve your issue, since you have your child theme active and ready, please follow the following steps below:
1] Using Notepad or TextEdit or Sublime Text or any text editor, please create a new file in your local machine.
2] Insert the following code into that new file
<div id="buddypress">
<?php do_action( 'bp_before_activation_page' ); ?>
<div class="page" id="activate-page">
<?php do_action( 'template_notices' ); ?>
<?php do_action( 'bp_before_activate_content' ); ?>
<?php if ( bp_account_was_activated() ) : ?>
<?php if ( isset( $_GET['e'] ) ) : ?>
<p><?php _e( 'Your account was activated successfully! Your account details have been sent to you in a separate email.', '__x__' ); ?></p>
<?php else : ?>
<p><?php printf( __( 'Your account was activated successfully! You can now <a href="%s">log in</a> with the username and password you provided when you signed up.', '__x__' ), wp_login_url( bp_get_root_domain() ) ); ?></p>
<?php endif; ?>
<?php else : ?>
<form action="" method="post" class="standard-form cf man" id="activation-form">
<label for="key"><?php _e( 'Please provide a valid activation key.', '__x__' ); ?></label>
<input type="text" name="key" id="key" value="<?php echo esc_attr( bp_get_current_activation_key() ); ?>" />
<p class="submit">
<input type="submit" name="submit" value="<?php esc_attr_e( 'Activate', '__x__' ); ?>" />
</p>
</form>
<?php endif; ?>
<?php do_action( 'bp_after_activate_content' ); ?>
</div><!-- .page -->
<?php do_action( 'bp_after_activation_page' ); ?>
</div><!-- #buddypress -->
3] Save the file named as activate.php
4] Upload this file to your server in the child theme’s folder wp-content/themes/pro-child/buddypress/members/
You will have to create the folder path since it does not exist in your child theme yet.
Please let us know how it goes.