Does an app's bundle ID change after App Transfer in the developer program and itunes connect?
Yes the app identifier changes and no the bundle remains in your scenario. Unless you copied the information wrong from the portal, 5E4D3C2B1A.com.company.app is what you’ll ship next iteration. 

When you submit and the app goes to sale, only the Team ID part of the app identifier will change and you’ll have the one time loss of keychain data the app stored. 

This could be minor or major depending on how the app was designed. 


https://developer.apple.com/library/ios/technotes/tn2311/_index.html#//apple_ref/doc/uid/DTS40014135-CH1-A_ONE_TIME_LOSS_IN_KEYCHAIN_DATA_WILL_OCCUR_IF_YOU_SWITCH_YOUR_APP_ID_PREFIX


If you have thousands of users or can’t be sure you are safe after talking to the previous Dev or inspecting the code, you might burn one of your paid support incidents with Apple to review the code and be sure you’re safe to go with the change.