So, in my case this way hepled: 1) I’ve replaced 'composer'
with 'author'
in functions.php
(in that part where connections are being registered) and 2) “edited” data in ${wpdb}_p2pmeta
using phpmyadmin (UPDATE <yourprefix>_p2pmeta SET meta_value = "author" WHERE meta_value = "composer"
or manually or like that).
Please, backup your data, please test in any way etc.