Yes, most facilities can deposit a check directly into an inmate's account, but the process has to be done correctly to avoid the check sitting unprocessed or being returned.
Do not mail the check directly without first calling the facility and speaking with her case manager or counselor. They will give you the specific instructions for that institution, including who to address it to, what information to include with the check, and what the facility's process is for handling checks sent from outside. Take notes during that call because the details matter.
The general process at most facilities is to mail the unsigned or endorsed check to the facility with the inmate's full name and ID number included, the facility then has the inmate endorse it, and the funds are deposited into their commissary or phone account. Some facilities handle this smoothly and routinely; others are slower or have more specific requirements.
The note about a prior check never being received is worth raising on that call. Ask specifically what the procedure is for verifying that a deposit arrived and was processed, so you have a way to follow up if something goes wrong again. Sending anything of value to a facility without a confirmation process leaves you with no recourse if it gets lost or mishandled.