SQVI queries are always assigned to the SAP users who created them, and cannot be changed by another SAP user. In remQ you can use SQVI queries created by another user (see https://www.voquzlabs.com/knowledge-base-remq/how-can-i-install-remq-and-test-it) if the name of the query starts with the prefix REM_. But only the user who created the query can change it, or the query has to be re-assigned to a new user. To do this, follow these steps:
In transaction SQ02 go to Settings -> Settings -> check Display System Objects.
Then in SQ03 go to Environment -> Query areas -> select Standard area (client-specific).
In the User group assignment field, enter the username into the User field, and click on change. Scroll through the list with the page down/up buttons and locate the user group(s) QuickViews: <username>. This was automatically created by the system for this user. Check the field and save.
The user will have access to the QuickViews of the selected users.