Note: Downloaded maps even work in Airplane Mode. (Highly recommended to save battery.)
How to do this:
On a computer, click on the link to the map shared with you.
At the top of the text box there will be three vertical dots. Select this and "Copy Map" to your own maps.
Now go to your phone and bring up the google maps app.
At the bottom you will see "Saved", Click that.
Scroll all the way down, and select "Maps."
Select the maps. Adjust the zoom and position of the map so that it is all in the screen.
In the "Search Here" bar type "ok maps".
Magically it will popup a screen asking if you want to "Download this map?". Do it!
You can set your phone into Airplane Mode and verify that it actually works.
Go to the main screen when you first start maps. This can be reached using the "Explore" icon as well.
Click your picture/icon in the top right of the screen.
This brings up a hidden menu. Select Offline maps.
You will see a list of your offline maps that you can manage (delete, rename).
You can create maps in here but the "ok maps" trick described above tends to be easier for me.