If you have an instance where you want to increase a public mailbox in Exchange 2013, follow these directions:
1. Determine which mailbox needs to be increased.
2. Get-Mailbox -PublicFolder -Identity Mailbox1 | fl prohibitsendquota
3. Now we will go ahead and increase the prohibitsendquota
4. get-Mailbox -PublicFolder -Identity Mailbox1 | set-Mailbox -PublicFolder -ProhibitSendQuota 21000000000
This increases the prohibitsendquota to approx 19.56GB. You may have to increase the prohibitsendreceivequota first to a value larger than 19.56GB. You can see that I set it to a value of 25GB first, before increasing the prohibitsendquota to 19.56GB