If your husband goes on Medicare in July 2020 and they backdate him, he will have Medicare for all of 2020, so he would not be eligible to contribute to his HSA in 2020.
But if he has not maxed out his HSA contribution for 2019, he has until April 15th to contribute more to his HSA.
NOTE: he must make it clear to the HSA custodian that this contribution is for 2019, otherwise, the custodian is required to apply it to 2020, which would be bad.
Also note that the annual HSA contribution limit is the sum of all HSA contributions made in calendar year 2019 and any HSA contributions made in 2020 for 2019 - so use all your fingers and toes to make sure that you don't accidentally exceed the annual HSA contribution limit.
If he hasn't contributed the $1,000 catch-up for being 55 or older for 2019, then he can do so, so long as he does it before April 15th.
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