Yes. For purposes of calculating health savings account (HSA) contributions, HSA-eligibility is measured on a monthly basis, based upon what the eligibility status is on the first day of each month.
For example: If an individual is only eligible from January 1 through June 30, the individual can put in one-half (six of the twelve months in a year or 6/12ths) of the maximum annual contribution for the year. However, if the individual is eligible from January 1 through July 1, then the individual can make 7/12ths of the maximum allowable contribution (because eligibility is measured as of the first day of any given month, and that would be seven out of twelve months).