iPhone 6/6+ - Error 53
Regarding Error 53, we've found that the issue is sporadic and doesn't affect all replacement parts, however when it does occur we suspect it may be an issue related to a new home button link cable (which frequently comes preinstalled on new full display assemblies). But, it is possible that a damaged part could cause the error since it's no longer recognizable to the OS.
Here are some articles in which we go into more depth regarding the topic:
In order to restore functionality, try using the original home button link cable. Otherwise, try reverting to the original display assembly (including original home button link cable) and the original home button assembly, then perform the update. Once the update is successful, then you can try reinstalling the new part(s).
For the iPhone 6, please refer to this guide here regarding the home button link cable. For the iPhone 6 Plus, we don't have an explicit guide, but the process is similar to the iPhone 6.