Does cooking with solar cookers preserve the nutrients in food?

Also does it modify or make the food more nutritious with solar cooker.

Not more than any other kind of similar cooking by radiant heat, like baking. There is simply no mechanism by which that could happen. Let's examine some claims I found from Google:

from http://www.greenbuild.org/uncategorized/3-reasons-solar-cooking-is-good-for-you-and-the-environment/

Solar cooking doesn’t use smoke that can contain carcinogens or microwaves that expose your food to potentially dangerous radio waves.

An electric stove produces no smoke (if you don't burn the food), and natural gas produces very little smoke. Were there smoke emitted by the stove, the area around it would be covered in soot, and the flame would be yellow from the carbon (the main component of soot and smoke) heated to incandescence in the flame. Further, the biggest cancer risk from smoked foods is not the smoke, but the nitrates frequently used to cure them.

If microwaves emit dangerous radio waves, the sun emits far more. That's why it's so bright, and so hot. I suppose you could be harmed by the microwave's radio waves if you manage to turn it on without shutting the door. Then again, you can cook your hand in a solar cooker, too. Or a stove. Come to think of it, cooking involves potentially dangerous heat. Huh.

Also: Does microwaving destroy nutrients in food? (summary: no more than any other cooking)

Plus, when you cook in a solar appliance, the nutrients stay in the food and don’t leach out. That’s because you don’t use water in solar cooking. And, the temperatures in a solar oven are moderate – around 325 F – so nutrients aren’t destroyed during cooking at a high temperature like on a grill or over an open flame.

This is also true of many other methods of preparing foods: baking, grilling, microwaving, frying and, don't involve water. 325 F is not an unusual temperature for baking, and most other methods can be performed gently, if desired.

To summarize: there may be benefits of solar cooking (a big one: it requires no fuel), but nutrition is not one of them. There's no way sunlight can add more nutrition to food that wasn't there to begin. Any nutritional benefits are not as much from solar cooking specifically as they are from not cooking by some less nutritional method. For example, any cooking method that is not boiling will not have the possibility of dissolving some of the food's nutrition.