You will need the Full Write Accounting permission to record entries, at the campus you are working in.
Short answer: One Church Software has no transfer between organizations. Each organization records its own side of the money in its own books, and a gift's organization never changes.
This is how it is designed to work, not a workaround. If your church pays the school, the church records a payment out in its books, and the school records a receipt in its books. That is two entries in two sets of books, and no single action does both.
Why it works this way
An organization is a separate legal entity, with its own EIN and its own books. Each one has to be able to report on its own, so a gift belongs to one organization for good, and an accounting entry never spans two. How do books work with more than one organization? explains how the books are kept apart.
What is refused
These are all refused across organizations:
Fund transfers between two organizations' funds. The message reads: A fund transfer cannot move money between two organizations' funds.
Entry lines from two organizations on one entry. Every line must use accounts and funds of the entry's organization.
Due-to, due-from or inter-organization transfers. There are none.
Payments, merges, bank feeds, budgets and combined checks that span organizations.
Paying bills of two organizations together. The message reads: These bills belong to more than one organization's books. Record each organization's bills separately.
Moving gifts to a batch of another organization.
Closing and posting batches of two organizations together, because the deposit account must belong to the batch's organization.
Moving a designation to another organization once it has gifts, recurring gifts, giving pages, keywords or campaigns.
Moving a pledge campaign to another organization once it has pledges or payments.
Merging designations or accounts that belong to two organizations.
Moving an entry that is reconciled, matched to a bank transaction or printed as a check to another organization.
What to do instead
In the paying organization's books, record the money going out, using that organization's accounts and funds.
In the receiving organization's books, record the money coming in, using its own accounts and funds.
Use the Accounting for: strip at the top of Accounting pages to switch between the two organizations' books. To move money between funds inside one organization, see How do I transfer money between two funds in the same account register?
What can still change organization
Some entries can still move to another organization, as long as nothing has locked them:
Campuses can be changed only on manual, fund transfer, register and transfer entries. Entries that are closed, or that come from a batch, a bill or a void, cannot be changed.
Moving an entry to another organization also needs it to have no printed check, no finished reconciliation and no bank match.