Much of that is incorrect.
He still will be getting a deduction for his mortgage interest and the property taxes, it will just be built into the installment sale rather than into rental income/loss. She will get a deduction for the mortgage interest on HER mortgage, but not on the property taxes as she will not be liable for them, since he would be holding the title.
Basically the net effect on his taxes would be little different than the net effect of renting the property. Rental income is offset by expenses (mortgage interest, property taxes other expenses) and Installment sale income is offset by expenses as well.
As a financial professional, you should be more careful.
Let's do the math. Assume his mortgage payment of $1,000 to the bank and she also pays $1,000 to him (either rental or mortgage payment). Assume taxes of $3,000 per year. (none of the assumptions change anything, but they allow an estimate to occur). For simplicity, I'll assume that they're early in the mortgage so most of the payment is interest and I'm calling the entire amount deductible. That is obviously not correct, but a more detailed analysis gets the same result.
He rents to her:
Her $1,000 payment is not tax deductible. He pays the taxes.
He gets mortgage tax deduction ($1 K per month) but he has rental income of $1 K per month. His net deduction is $3,000 per year (taxes). She pays him $12 K and he pays out of pocket $15 K, for a net expense of $3,000 per year. (He also has to pay for maintenance, so it's even worse). OTOH, all the equity is his.
Her net payments per year are $12 K, all non-deductible.
He sells to her:
Her $1,000 payment is tax deductible. She pays the taxes.
He gets mortgage deduction ($1 K per month) but he has mortgage repayment of $1 K per month from her, so his net deduction is zero. He has zero net expense.
She pays $15 K per year, but all of it is deductible. She is responsible for maintenance expenses. OTOH, all the equity is hers.
Now, there is undoubtedly SOME combination of tax rates and interest rates where it comes out a wash, but that would be purely coincidental. Mathematically, if you choose to make the mortgage payment the same as the interest payment, there is a huge difference between renting and selling.
Just like the 401K issue, taxes must be considered when making a long term financial transaction. Ignoring the tax issues does a major disservice to one (or sometimes both) parties.