Copying Lync conversations between accounts is very easy.
All we have to do is to copy them using Microsoft Outlook.
How to do it ?
select all conversations (b) from the Conversation History folder, from the old profile (a);
now, either use Ctrl+C to copy everything, either press the right mouse button (right click) and pull all the conversations to the new profile (c);
release the mouse button and choose Copy from the contextual menu.
After copying the conversations, we have to wait several minutes (depending on the number of conversations) until the Conversation History folder is synced.
After the sync operations, the conversations now appear in Lync.