We have two physical sites in our environment (suppose A and B). When we are trying to share desktop/programs via Lync 2013 from machines in same site, its working fine. However when we are trying the same from A to B or B to A, only the program sharing is working, where desktop sharing is not working with an error: "An error occurred during the screen presentation". Lync meetings and chat are also working fine for cross sites.

Any help would be appreciated!! 

Sound more of network related issue

please check is the relevant ports are open for client communication

https://technet.microsoft.com/en-us/library/gg398833.aspx

can you have peer to peer audio call between site a and site be user