ANSWER: This is one of those seemingly simple questions for which, unfortunately, there is not a simple answer.
First, consider the question from the perspective of the Bylaws. If the donation is in the budget that was approved by the members, or if the Board or Executive Committee has discretion under your PTA’s standing rules to make disbursements not authorized in the budget, then making a donation to another PTA would be consistent with the Bylaws. If the donation is not in the budget or not otherwise authorized, you would need to have the budget amended at a general membership meeting before proceeding.
However, the answer doesn’t end. You also need to review the application that your PTA completed when it applied to the Internal Revenue Service for tax exempt status. Because your PTA is tax exempt under Section 501(c)(3), the form that you completed is called the IRS 1023 (it’s an IRS 1024 for PTAs that are tax exempt under Section 501(c)(4)). The application sets forth the activities that your PTA told the IRS it would engage in, and the grant of tax exempt status is limited to those activities. Many PTAs’ 1023 speak to operating programs for the benefits of the students at XYZ school (i.e. the school with which the PTA is associated). If that’s the case with your PTA’s 1023, you would need to let the IRS know that your PTA’s scope of activities has expanded to include benefiting other students in your district or community. To do this you only need to submit a letter to the IRS when you file your next tax return(990 or 990EZ) explaining that your activities have expanded.
Finally, if the PTA (or for that matter any other organization) is not tax exempt under Section 501(b(3), then you should place a condition on the donation that the funds can only be used for a tax exempt purpose. Otherwise, your PTA could be considered to be diverting tax exempt funds for a purpose that wouldn’t qualify for tax exempt status.