If someone is not available to speak for themselves, a person might say "on the behalf of *so and so* I would like to thank you...", or "on the behalf of *so and so* I am informing you...", or "on...
Indemnity, indemnify (as I understand it) is protection from loss, and to make whole, after a loss has been sustained.
On Behalf of would be the person the sum is being paid for/in your...