The total permissible contribution between you and your your wife is $7,838. However, your contribution to your own HSA is limited to $4,988 based on your 7 months months of eligibility. The remaining $2,850 of the overall contribution limit would have to be contributed by your wife to your wife's HSA. With your wife's employer having already contributed $1,167 on behalf of your wife and you having contributed $4,988 to your own HSA, that leaves $1,683 that can be contributed to your wife's HSA without exceeding contribution limits.
Alternatively, the entire $7,838 contribution limit could be allocated to your wife, so she could make a $6,671 additional contribution to her HSA if you contribute $0 to your HSA.
