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a prorated portion of the annual HSA can be made for each month you are covered by an HDHP.  however, if on 12/1 you are covered by an HDHP you can make a full year's contribution but then you must be covered by a HDHP for all of the following year. 

from pub 969 for 2022

Example 1. You become an eligible individual
on December 1, 2022. You have family HDHP coverage
on that date. Under the last-month rule, you contribute
$7,300 to your HSA.
You fail to be an eligible individual in June 2023. Because
you didn’t remain an eligible individual during the
testing period (December 1, 2022, through December 31,
2023), you must include in your 2023 income the contributions
made in 2022 that wouldn’t have been made except
for the last-month rule. You use the worksheet in the Form
8889 instructions to determine this amount.

January 2022 . . . . . . . . . . . . . . -0-
February . . . . . . . . . . . . . . . . -0-
March . . . . . . . . . . . . . . . . . . -0-
April . . . . . . . . . . . . . . . . . . . -0-
May . . . . . . . . . . . . . . . . . . . -0-
June . . . . . . . . . . . . . . . . . . -0-
July . . . . . . . . . . . . . . . . . . . -0-
August . . . . . . . . . . . . . . . . . -0-
September . . . . . . . . . . . . . . -0-
October . . . . . . . . . . . . . . . . -0-
November . . . . . . . . . . . . . . . -0-
December . . . . . . . . . . . . . . . $7,300.00
Total for all months . . . . . . . . $7,300.00
Limitation. Divide the total by 12 $608.33
You would include $6,691.67 ($7,300.00 − $608.33) in
your gross income on your 2023 tax return. Also, a 10%
additional tax applies to this amount.