You need a new AppleID that has access to iTunesConnect from this other organization. If you have access to an account with administrator rights in iTunesConnect for this organization, log in to it and go to the "Users and Roles" section. Since this is an organization, there are several users. And next to "Users" there is a plus button:

Click the plus. There you can enter a new username, last name and email address (it will be used as Apple ID). You can also use an existing AppleID that is not yet registered with iTunesConnect (iTunesConnect will show you a warning, but that's fine).
This will create an account capable of publishing applications for this organization.
Then, in the Xcode settings (Accounts tab), you add a new account.
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Then, when you submit the application, you will be asked to select an account to send:

Unfortunately, I don’t remember if I need to register a new AppleID in DeveloperCenter, as well as in iTunesConnect. But even if you need to do this, it should be easy to do: you simply add it as another identifier in the organization (you need to have the right to invite new users to the organization for this, of course).
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