Hi
Do the following
In the Power Apps UI, click the Environment drop down, select the Vertical 3 Elipses to the right of its name
Select go to admin center
When you get there, on the right hand side under Security, select All Users
This will open up a list of all the users who are IN the environment and able to HAVE roles associated to them, which is what you want.
In the Filter/Search on the Top Right, start to type their name and see if they are IN the environment.
If they are NOT you first have to get them a license and Add them to the environment
If they are, then here is what you need to do.
1) Assign them a Role that has permission to read/write that table. I cannot tell you which role, because its a custom table, you need to MAKE one
2) as you make the new role, make sure to also give them basic user role if they dont already have it
3) in the new role, you have to assign privs to read and write to those custom tables.
To get to Custom Roles
go back to the main Admin Environment screen.
In my picture above you can see where it says Security Roles, click See All
Click on New Role
Now you have to assign the role a Name and select the business unit, but I cannot tell you what to set the Members Priviledge, you need to ask your admin if you want Direct User or Teams. I am going to assume you want Direct User though
As an Example I created a role called Demo Role
It will Immediately take me back a screen and now it will list all tables. and so I can now set the tables it can do things too. You want to Search for your Table
And set the privs.
Thats how you do it.