Multiple Spell Loadouts
To help with bookkeeping for full casters with lots of options I think the best approach is to create multiple Spell Loadouts. A fully prepared list that is suited for certain situations. For example:
- A combat spell list. This is the list to prepare when you expect a lot of combat. Look for damage spells and battlefield control.
- A utility spell list. Prepare this list when you no there is low chance of combat, but could need ways to bypass traps, trick guards or open doors. Include social spells, detect magic and other utility spells.
- An allrounder list: Prepare this list when you don't know what they day ahead will hold. Include your most effective combat spells and your most often used utility spells.
- An explorer's list: The spell your need out in the wilderness are quite different to the ones you need in town. Prepare travel spells, things to increase movement, find resources and particularly spells that allow you to take long rests in magical safety.
They can then simple choose which list to prepare for the given day. Reducing their options from dozens to 3 or 4.
I have used this successfully with the Wizard in my party until he got a better grip on his class and now no longer needs it. Though he does have a preset list that he brings most days.
Either purchase the official ones or create your own. These are hands down the easiest way to remember how spells work. My players all have binders with card pockets in them. They each have their own system for how they sort them but having the spells at the table without checking the book is a big plus.
Additionally having card pockets in binders gives me an easy way to hand out items. I create item cards in the same size to hand out at the table. I even have cards for potions, No Card = No Potion. Reduces the book keeping of remembering how many you have.
Spell Slot Tracking Sheet
I haven't had to use this one since my players were new but it might be something you could use.
Create a simple template with the correct number of checkbox per level as they have spell slots. They can them mark then off on the sheet quickly and easily. You can either just print a bunch of these, or print one, laminate it and use an erasable marker. Though this is risks rubbing off between sessions.
On top of needing help with book keeping it sounds like your player may be a problem player. They may not be if them being on their phone doesn't disrupt your table. However, if this is behaviour you wish to correct we have lots of good questions in how to deal with this sort of things, check out:
It is important to remember that there are multiple play styles and potentially the player simply isn't interested in non-combat scenarios. You should talk to the player and try to figure out why. Maybe they feel uncomfortable roleplaying? In which case the advice in the linked question will help.
Whatever the reason, you can't resolve it if you don't know what it is. Remind them that you want them to have fun and that if non-combat isn't currently fun for them you would like to find a way to improve it.