Can money received as a gift be used to fund a Roth IRA?

TL;DNR version: Yes, money received as a gift can be contributed to an IRA (whether Traditional or Roth) but to be eligible to contribute to an IRA for any year, the IRA owner must have received compensation (essentially, money earned by the sweat of one's brow) during that year.

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The source of the money (e.g. wages, savings, gifts, cashing in US Savings Bonds etc) that is used to fund an IRA is not important: what is necessary is for the OP's girlfriend to have compensation (compensation generally means earnings from working) which is not just what appears on a W-2 form as salary or wages; it can be earnings from self-employment too, as well as commissions on sales, alimony etc (but not earnings from rental property, pensions and annuities, certain types of partnership income etc). The reason is that Roth IRA contributions are limited to the smaller of her compensation and $6000 ($7000 if age 50 or more) for 2020 (and for 2021 too).

Be aware that almost all IRA custodians will accept IRA contributions without enquiring as to whether the IRA owner has earned income or not (or maybe somewhere in the fine print that nobody ever reads before clicking the Submit button it will say something like "By clicking Submit, I am certifying that I have sufficient earned income to support this contribution."). For those who make IRA contributions in excess of what they are entitled to make, the fit will hit the shan (as Dr Spooner was fond of saying) when at the end of the following May, each IRA custodian sends Form 5498 to the IRS (with copy to IRA owner) telling the IRS how much has been contributed to the IRA by that person, and the IRS matches up these numbers with what that the owner's tax return says. This reconciliation catches people who contributed more than they are entitled to contribute, and various undesirable consequences follow.

Note that lowly-compensated folks can contribute their total compensation to their IRA if they choose to do so. But what about the fact that the take-home pay is less than the total compensation because of Social Security and Medicare tax, not to mention income tax withholding? How can people earning less than $6000 contribute all of it to an IRA? Well, that is where savings or earnings from rental property etc can be used to fill in the shortfall between take-home pay and the total compensation amount to be contributed to the Roth IRA.

Note that at the upper end, high-earners are prohibited from contributing to a Roth IRA at all. Also, while high earners can contribute to a Traditional IRA, they cannot deduct their contribution on their tax return. That nondeductible contribution is not taxed when withdrawn but any growth of that money is taxable when withdrawn from the Traditional IRA. See this answer for details.