Google Ads - adjust conversions by api requires customer ID

on my website, I'm using GTM (Google Tag Manager) to upload click conversions, for Google Ads, immediately after user purchase.

Now, I'm using Google Ads REST api for some other operations. I want to use it, also for adjusting (modifying) conversions offline, after the purchase. But, REST api requires doing that by Customer (account) ID.

But because I have multiple accounts, I don't which one of them is the correct, I only have the data relating to the order - order id, gclid, order time, etc.

I looked after a way for implementing that, but couldn't find.

Is there a way to implement conversion adjust with Google Ads REST api, given I have multiple accounts and I don't which one of them is the correct? But with other conversion details like gclid and order id?