Modules
The modules are specified in App's command 2. There is a byte[40] header of sorts that describes the module. The byte[40] can be broken down into
{
  int 'auth'
  short unk
  short locale - EU or US (apparently SB for s2 modules)
  byte[32] moduleId
}
After this header there is a short, use currently unknown, and then after the short is the data passed into the modules packet handler, which is the 3rd function (starting from 1) in the modules vftable. It is up to the module to decide how to handle this data.

Password.dll
Performs account data verification, uses SRP6a with SHA256 as the hashing function
If verification successful, stores the byte[64] sessionKey to the buffer with id 0xB6E372AE. Battle.net.dll checks this in sub_3C919E40 and sends an error packet if the data is not there
Hashes:
23451d428a1671e27635e923e9acfd6f8a883acb1f8e6b2a4152f037e5841594 - Password.dll, Augustus
5a22ce74646016952737205c0ae4f9a55cfa69e1aa1ef4469d5aa74f3dcdbb1b - Password.dll, Vesuvious
Data:
byte opcode
The data that follows depends on the opcode
Opcodes:
0 - S-C: Battlenet::Client::Stalker::ChallengeResponse
    Contents:
      byte[32] m_accountSalt
      byte[32] m_passwordSalt
      byte[128] m_serverChallenge
1 - S-C: Probably a reconnect challenge
    Contents:
      byte[32] m_passwordSalt
      byte[128] m_serverChallenge
      
2 - C-S: Battlenet::Client::Stalker::ProofRequest
    Contents:
      byte[128] m_clientChallenge
      byte[32] m_clientProof
      
3 - S-C: Battlenet::Client::Stalker::ProofResponse::Result::Success
    Contents:
      byte[32] m_serverProof
4 - S-C: Battlenet::Client::Stalker::ProofResponse::Result::Failed (this may also be opcode 2, S-C)
    Contents
      byte m_reason - maybe byte? dunno

      
Thumbprint.dll
Performs some other kind of verification.
Reads buffer id 0xF8AC9F37 (16 bytes) from battle.net.dll, then creates a sha512 hash of those 16 bytes and the string "Thumbprint.IPv6". Then uses this buffer and performs RSA verification using the exponent/modulus hardcoded in the module. Note that the modulus's are different between the Augustus/Vesuvious branches
If verification successful, stores a 1 to buffer with id 0xA2057DF4. Battle.net.dll reads this and sends a packet if value != 1, sub_3C919E40
Hashes:
36b27cd911b33c61730a8b82c8b2495fd16e8024fc3b2dde08861c77a852941c - Augustus
61292e01a368a60a91d4f8d6903fd5968de21bdab8fdc8f36ca0a05cc11bab53 - Vesuvious
Data:
byte[512]