How does my husband go about going Active Duty Infantry from the Reserves?

Step 1. Review the prior service accession business rules to determine if there are vacancies for his grade and MOS at https://m.goarmy.com/careers-and-jobs/current-and-prior-service/continue-serving/return-to-active-duty/prior-service-business-rules.m.html.
11B for E-5 is currently available for Soldiers already MOSQ and as a reclass option.

Step 2. See Regular Army recruiter to request a DA Form 368, Conditional Release, signed by that recruiter, requesting release from your Reserve service obligation contingent on your acceptance to active-duty. This may be a challenge, or maybe even non-starter for your Commander considering they've just paid for your reclass training. The conditional release approval authority is first General Officer in your chain of command.

Step 3. If the 368 gets approved by your chain of command, return it to your recruiter and wait for orders.

I sure wish I knew the process so that I might be able to help you and your noble husband. I have a former Air Force Reservist friend whom I shall inquire with. Perhaps he can help. He's not on RP but I will share his response if he has any pertinent ideas or information.

Simple answer is have him talk to a career counselor