Not the way you suggest. An HSA, like an IRA, belongs to one and only one person, and spouse #2 can't make a funding distribution from an IRA owned by spouse #2 into an HSA owned by spouse #1.
However, spouse #2 may be able to make a qualified distribution into an HSA owned by spouse #2, if spouse #2 is eligible.
If spouse #2 is covered by a family HDHP and has no other disqualifying coverage, then spouse #2 is eligible to make contributions to an HSA even if the HDHP is in spouse #1's name. Therefore, if your only insurance coverage is your spouse's HDHP, then you can open and contribute to an HSA. You can do that at many different banks if your employer does not offer it internally, you can shop around for the lowest fees.
Your contribution limit for 2020 is $7100, plus $1000 if you are age 55 or over. Note that the $7100 is also your overall family contribution limit, but the $1000 catch-up provision is specific to each person. So if you and your spouse are both over age 55, then you can contribute $9100 in total--that's $7100 that can be split between the spouses' accounts any way you like, plus $1000 catchup that can only go into spouse #1's account and $1000 that can only go into spouse #2's account.
So spouse #2 can do a QHFD from spouse #2's IRA into spouse #2's HSA. The maximum amount is $7100, or $8100 if spouse #2 is age 55 or older. Then spouse #1 can make a regular contribution into their HSA, but only up to $1000, since spouse #1 seems to be 55 or older based on the question.
