The general rule is that such a setup cannot be made to work for the purposes of communicating with a TI calculator through the legacy I/O port, because AFAWCT, most USB / RS232 DB9 adapters don't provide the direct wire access that TI's custom half-duplex protocol needs.

At some point, someone mentioned that his PL2303-based adapter could do it, so I requested more information about it, and bought that particular
model. However, I never actually tested a known working BlackLink / $4 cable against it, so I can't point anyone to a precise model of an USB / RS232 DB9 adapter which I know works with them.

Nowadays, libticables provides a way to define the device corresponding to a cable handle, so that e.g. /dev/ttyUSB0 can be used instead of
/dev/ttyS0 on Linux. TILP doesn't provide an UI for the user to enter an alternate device, though, so users still have to resort to symlinks on Linux.

The GrayLink is a different matter. Unlike the BlackLink / $4 cable, it speaks a standard RS232 protocol, and performs two-way adaptation with TI's half-duplex protocol on the calculator side, without the computer being aware of TI's protocol.