You say you want to decompress the data coming from A so B can do incremental backups and recovery. Were A's data not encrypted this would make perfect sense. But A's data is encrypted and that changes everything. Let's think this through.
Let's say A compresses its data and then encrypts it. And let's say B could somehow decompress the data from A without decrypting it; it can't, but let's suppose. B now has A's decompressed, but encrypted, data. It has, effectively, random bits.
In order to do incremental backups the latest versions of files from A must have something in common with their older versions. But even the smallest change to the unencrypted data will completely change the encrypted data. There are no increments. Each encrypted version of a file from A has nothing in common with the previous version, else you'd be able to extract information. B can't do incremental backups on encrypted data whether the original was compressed or not.
Similarly to do data recovery B must have some sort of pattern to look for. Encrypted data is effectively random. B cannot do data recovery on encrypted data, there's no pattern to look for.
So, from B's perspective, compressed and encrypted data from A is the same as encrypted data from A. It's just smaller.
The integrity of your backup can be handled by conventional means: multiple redundant backups, RAID, off-site backups, and so on. As for incremental backups, I don't think it's possible here. Fortunately that's just about saving disk space. Consider off-loading older versions to cheaper, slower storage.