In general, she can play the Sims 4. It won't be great but it will be playable. I recommend you ensure the laptop has two sticks of RAM in it for best performance. Two sticks of RAM means the RAM will be running in dual channel mode (full speed) rather than single channel mode (half speed). It should be easy to remove the underside of the laptop to see if it has a single 8GB stick of RAM or two sticks of 4GB RAM.
If there is only a single stick of 8GB RAM then it is best to purchase as 2nd stick of 8GB RAM so that the RAM runs at full speed and can improve not only overall performance, but also game performance. Pairing up a 4GB stick of RAM with the 8GB stick will make the RAM run in asynchronous dual channel mode. It will be better than single channel, but not as good as "real" dual channel mode.
Below is a link to an 8GB stick of RAM that would be compatible with your laptop.
I found the below-given configuration to be recommended for sims 4 on the official website of EA:
Operating system: 64 Bit Windows 7, 8, 8.1, or 10
Processor: Intel Core i5 or faster, AMD Athlon X4
Memory (RAM): 4 GB RAM
Hard drive (free space): At least 9 GB of free space with at least 1 GB additional space for custom content and saved game
DVD drive: DVD-ROM drive required for installation from disc only
Graphics card (video): NVIDIA GTX 650 or better
Direct X version: DirectX 9.0c Compatible
Note: it's the recommended configuration, not the best configuration for playing Sims 4. Obviously, if your girlfriend is a casual gamer, then the laptop you mentioned above might be able to run the game but for sure you'll definitely not get a good experience.
Since you mentioned that your budget is near about $400, you can also check out "Dell Latitude E7440"
You can check it out here: https/www.amazon.ca/Dell-Bluetooth-Professional-Certified-Refurbished/dp/B075Q5FFSX/