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I am not sure if there is any time line to apply for secured card. Sooner you apply the sooner they will start reporting. It will probably take 12-18 months for effect start showing on the scores. You mentioned he is pre-approved for Discover secured card. I would apply for it and get it. OpenSky is another secured card you can easily get with out hard inq on the credit report. They approve every one. Start with OpenSky and Discover secured card and it start reporting.
Now for the secureds unless you already have open revolving accounts. You need 3 revolvers to help drive Fico score in a rebuild, two open is a good start