I have more than five years of scrog experience so here goes.
It is most common to start training through the screen during the veg stage. Then during the initial 2 to 4 weeks of the flower stage training continues in what is known as the growth spurt. Training becomes unnecessary after the growth spurt.
In your circumstances I suggest the following. Move the plants from the veg area to the flower area 1 to 2 weeks earlier than you normally would do. However do not switch to 12/12 at this time. Continue with the 18/6 or 24/0 light schedule and the veg nutes program you would normally use. Even though you will now be under the HPS light the veg period will continue just fine. Start training through the screen right away and continue training until the screen is 50% to 75% filled (depending on strain and observation) and only then make the switch to 12/12 and continue training as the plant fills the remainder of the screen. The growth spurt during the first 2 to 4 weeks of the 12/12 flower period will stop and the training will be discontinued at that time. The first couple of grows you try you are better off switching to 12/12 a little early (based on screen fill) rather than a little late. An overfilled screen can lead to problems so you want to get a few good grows with scrog before you try to maximize screen fill techniques. During the growth spurt remove any growth that is below the screen as it will not be productive due to lack of light and you want all of the plants productive energy available to the part of the plant above the screen.
In my current grows I just change the light rather than moving the plants but if you must move the plants the methods I have described above will be very helpful. Don't worry that part of your veg period will be under HPS lighting despite others insisting that you must use different lighting for veg than for flower. I have personal knowledge of some very successful growers who use HPS for both veg and flower. I personally use 6400K for veg and 3000k for flower and just switch the lights when I switch to 12/12 and change nutes.
Never argue with a fool: 1) People watching can not tell who is who 2) They will drag you down to their level and then beat you with experience