You would be surprised how often people are afraid to acknowledge the truth of the matter because it's scary to them, too -- what your friend is experiencing is awful, and forcing them to see the bright side of their loved one's death is even more awful. Acknowledging the crappy situation is what makes grievers feel validated. I recommend something simple like this:

"Hey, I'm really sorry this is happening. It really sucks." Then, hug them, if they'll let you. 

You know how before their loved one was dying or dead and you guys used to hang out and talk about nothing at all and have the best time? They still really want to do that, but have no idea how because all they can think about right now is, "HOLY SHIT, MY MOM IS ACTUALLY DEAD." 

Don't invite them to your house, because they'll likely cancel because grief can actually physically hurt you and make you sick. What you'll need to do is come over to their house, and preferably with some type of snack because they'll likely not be eating as much. Ask them how they're doing, and then listen if they want to talk. If they don't, then just act like life is normal and if possible, invite a situation where laughter is on the menu, like maybe a Netflix show they think is really funny. They may just really need to laugh. Also, the release of laughter might release their emotions, and you may get them to open up about the loss. If they do, then repeat step 1. 

If they don't want to laugh, then respect that, and find a way to be there for the more mellow moments. Sometimes, they just really need someone in the room that is stable, to remind them that everything is fine regardless of how much pain they feel. 

One thing that happens during grief to a lot of people, is they become shitty friends. They can't help it. They're in a lot of pain, and everything sucks, and you just need to be patient as they bail on you to hang out, help out, be there for something many many times. Sometimes they'll have improper control of their emotions. It's all a part of the painful healing process. When the pain finally subsides, you'll notice they're more dependable, and easy to be around. And the last thing they need, is for you to make their grief about you. It sucks, but you just have to be the bigger person during this time. You will need them to one day, and if you push them away during their grief, they won't be around later. 

Grief comes in its own way, and time. Not every person reacts with instant sadness. Some are numb to it for years. Some take weeks, and some process it really fast. Do Step 2 often, to get a feel for how they're doing. If you stay close to them, you'll be able to tell if/when they are falling apart. 

And remember, whenever you need to say something... refer to Step 1. 

Grief is hard. There are losses in this life that we never get over. Living life along side people we love, and having them die, is something you never fully process. You know they're dead, and you know they're gone, but they never fully feel gone. So, expecting a person to "just get over it" on your timeline is a thinking error. Grief takes its own time, and even though someone is ok now, they're not over it, and they never really will be. You don't get over the people dying that you love. You can't. Your love still exists even when they don't. So, it is completely vital to the health of your relationship with a griever that you acknowledge this important fact, and let them heal. You only know how it feels once you've entered the grief club, and to get there, you have to face a big loss.

Remember, grief takes time, just try to love them through it, and as I said multiple times, when in doubt, always refer to step 1.