If you issue a FULL backup C without COPY_ONLY between A and B, then, you break the previous log chain A to B.
Full backups do not and never have broken the log chain.
It's trivial to test and, if you want, I can find a blog post from the former program manager of the Storage Engine stating and proving this.
The only things that break the log chain are:
* Switch to simple recovery
* Backup log with nolog/truncate only
* Deleting a log backup (won't stop you taking log backups, will stop you recovering with them)
According to Microsoft, you should backup log after the Full backup C to establish a new log chain.
I need to write a scathing email to either the author or the MS documentation people if such an official recommendation exists
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: Discussions on DB performance with occasional diversions into recoverability
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