A.7.22 When I put 32-bit PuTTY in C:\WINDOWS\SYSTEM32 on my 64-bit Windows system, ‘Duplicate Session’ doesn't work.

The short answer is not to put the PuTTY executables in that location.

On 64-bit systems, C:\WINDOWS\SYSTEM32 is intended to contain only 64-bit binaries; Windows' 32-bit binaries live in C:\WINDOWS\SYSWOW64. When a 32-bit PuTTY executable runs on a 64-bit system, it cannot by default see the ‘real’ C:\WINDOWS\SYSTEM32 at all, because the File System Redirector arranges that the running program sees the appropriate kind of binaries in SYSTEM32. Thus, operations in the PuTTY suite that involve it accessing its own executables, such as ‘New Session’ and ‘Duplicate Session’, will not work.