I’m confused. Is your wife eligible for her own Social Security benefits? Is she already receiving them?
She can get the difference of half of your SS benefit, or her own, whatever is greater. They will apply the difference to her benefit. BUT she must be at HER full retirement age, to get this 50% benefit. If she starts collecting earlier, the amount is reduced. Read this explanation.
And when you die, she can get your full benefit if it is greater than hers.
I suggest you go to www.MaximizeMySocialSecurity.com to get the correct answers to get the most benefits for her. Most people you might talk to at SS don’t have the knowledge to do this correctly!!