CGT cost base on vested shares?

Good day, As part of a long term incentive scheme, my wife is granted restricted shares in a US publicly listed company. The shares are granted at a price of zero and vest in equal instalments over the subsequent 3 years, if she remains an employee. On each vesting date, the shares vest at the closing market price on that day (which becomes the vesting price). Upon vesting, her employer automatically sells sufficient shares to cover both her income tax and employee’s national insurance. Am I correct that once the shares have vested, the “cost base” for CGT purposes becomes the vesting price (and not zero)? The reason I ask is because her broker shows the cost base of the vested shares as zero. That does not seem correct as she has already paid income tax on those shares - the difference between the grant price (zero) and the vesting price. Please could you clarify what the cost base should be on the vested shares? Much appreciated, Jason

Hi Jason Spilkin,
Yes,the cost price will be the vesting price on the day they vest/mature.
Thank you. 

much appreciated