Common Application Teacher Recommendations

My DSs (twins) have asked teachers for recommendations for all of the schools on their common applications a while ago.

If either son was to add one more school at this late date, do the teachers have to complete a new recommendation or will the new school just access the recommendations?

Or, I guess a better way to ask this is: do teachers write a separate letter of recommendation for each school on the common application or is there just one letter of recommendation that all schools access?
Thanks!

They write one letter.

Thank you!