As the Home for Good team join the new Slack, they will be added into all the general channels such as prayer, workchat, allstaff, etc. They will need adding (or re-adding) to restricted channels though.
If you already have a channel that has a Home for Good member listed as "external" then you'll need to add their new account to the channel and then disconnect the external ones.
Click on the channel header
Then go to the Members page and add people by searching in the Find Members box
Be sure to select the internal one. This will be the one WITHOUT the Home for Good logo
Once everyone is readded, you can then remove the shared connection which will stop the channel showing as external. To do this, go to the Settings page, click the three dots next to Home for Good and select "Remove..."