I have transferred properties into an LLC while I still have the mortgage.

This is because lenders are primarily concerned with the income-producing potential of the property when determining its value.In regards to your second question, it is possible to buy a property from yourself or transfer ownership between entities.

@Jason Carter I owned two B&Bs for years which provided a nice lifestyle and loads of skills none of which were transferable to a real life job situation.

Can I transfer the price quotes to someone else?

We are trying to put my name on the deed and take her off without her losing her benefits and avoiding transfer taxes.

Note: We put to the side any buyers who have "bought" multiple properties but it turns out those were all transferred on the same day, since those may just be an inheritance or entity change.

What I love about ADU is if it's separate there is more privacy and less noise transfer.

Adding your first property to an existing LLC is simpler than forming a new LLC and transferring ownership later.

Carryover basis for gifting is one major consideration, but you may also wish to consider what transferring the value of the property now at a relatively lower value would do for her taxable estate and any possible estate tax owed at her death. 

I also had a hard time transferring money internationally, so kept most of it in Canada, and saved up for a downpayment while working full time here.