if it were the other way around t(at the start of the year - non-limited FSA) the answer would be you could not start an HSA because the FSA could be used to pay expenses incurred at any time during the year representing coverage under a non-HDHP.
An FSA can only reimburse expenses incurred during the participant’s period of coverage. The period of coverage is the period of the FSA plan year in which the employee is enrolled. Thus any expenses incurred before or after the employee’s FSA period of coverage are not reimbursable. so if the FSA has a calendar year it could be used to reimburse expenses that you incurred for the months for which you contributed to the HSA. thus your HSA would not be allowed (the FSA would represent non-HDHP coverage). it would seem that an FSA contribution would be allowable but then you would have excess contributions to the HSA.
however, I have not read the employer's plan so maybe there's some provision in it that bars the FSA for you. you need to talk to your employer and get specifics.
