Have the User search bar above the Context entry. It should be intuitive that a new call or text has the recipient search at the top, then the message context and then the message paragraph. A lot of users type the user into the context entry, it's not visually clear.
Please note that as of Platform 6.4.0, the web directory search will automatically open with the search bar highlighted, which should somewhat reduce the confusion here. When navigating into groups and nested groups, we want to preserve the location of the search bar and have the group you are searching in take precedence, so unfortunately changing this location is not something we are considering. Thanks again for the great ideas!