Yes - the mortgage company almost certainly has to allow you and/or your sister to "assume" the mortgage. But the real issue sounds like it lies in a different direction. It sounds like the home is the bulk of your mother's estate. The question is "how does the estate pay its bills?" and "how do you and your sister get your inheritance".
Let's take a fictitious (and oversimplified) example. Let's say the home is worth $150,000 and $50,000 remains on the mortgage (leaving $100,000 in equity in the home)... but that's essentially all of what she had left when she passed away. Then we'll assume that there's ~$5,000 in probate and legal cost and that your mother left her estate equally to the two of you.
If that was $100,000 in cash it would be pretty easy. The attorney would take his $5,000 and you and your sister would each get a check for $47,500. If the two of you sold the home, it would still be straightforward (though no longer "easy" . You would pay about $9,000 in real estate commissions and the $5,000 to the attorney/court... and you would each be left with $43,000. But you would have to find somewhere to live.
But it sounds like you want to stay in the house. So the real question is how your sister gets her inheritance and how the attorney gets paid while the home stays in the family. If you don't have other assets to pay those expenses... you may be forced to borrow against the home, which probably involved refinancing (but might work with a smaller/cheaper home equity loan/line).