I am in corporate HR so will add my two cents after 30+ years negotiating salaries.
First of all- just because STATISTICALLY women are paid less than men, does not mean that every single woman in the workforce is being underpaid, and therefore, is required to negotiate her salary before accepting it. This is a very common fallacy. There are a lot of organizations which have lockstep type compensation systems, and therefore whether you are male, female or neither, you are going to be paid the same starting salary at your particular band and skill level. And of course, there are successful women who make more than the men, at that same level, and uber successful women who outearn men with even more experience. The paygaps which make the headlines are aggregated data based on millions of workers- not any particular woman being paid less in a particular role. And the numbers are moderately skewed because of women clustering in lower paid professions-- nursery school teachers make less than Firefighters in most parts of the country.
So asking for more just because you are female with no understanding of how this organizations comp works is bad advice IMHO
Second, most big organizations use a “Total Comp” system, although there are many other names for it. That means if your starting salary is 75K, your company paid healthcare plan is worth 15K, your annual bonus is going to be 5-15K depending on your performance, and the company contribution to your retirement plan is 7.5K, the number that shows up as your “total comp” is the sum of all these things- even though most employees fixate on the salary (to an obsessive degree in some cases, since some parts of the package are tax advantaged whereas an extra thousand dollars in salary won’t net the employee an extra thousand bucks.) So without an apples to apples comparison of current pay vs. the new offer, it’s hard for the hiring manager to hear “this is less money than I’m making”. Maybe the new company requires zero contribution for a better healthcare plan? Maybe the new company is paying 10% towards a retirement plan which vests immediately, vs. the old plan which matches 3% and has a multi year vesting schedule.
Third- agree with the advice to put the request in an email. It’s always good to have the benefit of time- on both sides. It’s too easy to lose track of the argument on the phone, and it is a little disruptive to the hiring manager if he/she is caught unawares by a phone call coming in the middle of the day. If someone MUST do it over the phone, at least send an email with a heads up- “Hi Joan, I’m so excited about the offer! Can we set up a 15 minute call to review the numbers and for me to give you some context about my current salary?”
So to the OP- if it were me I’d encourage my daughter to do some research first. Glassdoor is moderately helpful. Asking colleagues who they know who work at this organization- or have worked there in a recent past. See if someone will spend ten minutes on the phone to explain how the comp works. If this doesn’t work, then schedule time with the person who made the offer to say “I’d love to understand how your compensation system works”. Some organizations are more transparent than others, but this is not an offensive question to ask.
Your D may discover that the organization gives reviews and raises regularly and that high performers are accelerated quickly. Or she may discover that getting an extra 10K now means that she’s topped out in her band, and won’t be seeing more money for two years. Or she may discover that the organization is a hot mess, with no comp strategy at all, and that you’d better get everything you want upfront (which a former employee may candidly tell her- the place is a land grab).
I worked for a company once which pegged cash comp at about 80% of what the market leaders in the field were paying. It was a little frustrating to hire people, because our offers were generally disappointing the people we tried to hire. BUT- turnover was really low, nobody ever left, we’d hire for new ventures which were inevitably successful which was always fun to recruit for and to talk about. Quality of life was high, people respected their colleagues and adored/revered their managers-- really, the only downside was the cash. The benefits were unbelievable and progressive (one of the first companies in the US to extend healthcare to domestic partners without regard to gender, generous adoption policies, IVF included in medical, etc.) And good benefits are expensive, so on a total comp basis the packages were more than competitive.
When the labor markets got tight, salaries ratcheted upwards in order to retain people, attract the new hires we needed. During recessions, things stayed flat. During recoveries, things moved higher but slower than competitors.
I don’t know if I’d have managed comp in the same way if I’d been in charge- but it was a perfectly viable strategy in its own way. You don’t like the money? Go somewhere else where they’ll work you like a dog and disrespect you at the same time. And good luck getting paternity leave if you adopt a baby. You’re OK with the money? You’ll have a wonderful professional life with good work/live balance. It’s a choice.
Good luck to the OP’s D!