Congratulations!
Your son cannot enter the UK until the start date on his visa, which is 8th January 2020.
Also, he doesn’t have only 30 days to enter - he can enter any time from Jan 8th to April 6th 2020 (note that Jan 8th is the date I said it would be made valid from, as it is 7 days before your requested date of Jan 15th, so there was no need to worry that it would start in December

- though even if it had, it wouldn’t matter because he has until April to enter the U.K. anyway

).
There will also be no BRP to pick up.
This is because the 30-day vignette and BRP are only issued for visas valid more than 6 months. As his visa is valid for only 3 months, he just gets a visa sticker which is valid for the entire length of the visa (which is also why there is no approval letter, because those are only issued for visas where there is a BRP to pick up).
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