Set relationship between new object and existing ones - ios

Question

I've got this problem with Core Data and I don't know where to go with it... Couldn't find any questions similiar to mine so here I am asking you this one:
I've got a Core Data Model where I have a couple of Entities but what's most important there is the central point entity called Activity and other entities are in relation with this one. One of those is Group entity. There is a many-to-many relation between Acitivity and Group tables.
Before I get any Activity from backend I need to select group for which Activities I want. This way I need to fetch and save to the database Groups before anything else - that's fine...
But after saving Groups I need to fetch Activities and each activity has many Groups (which are already in Core Data) and I need to estabilish connection between those.
I assume that I need to fetch all Groups and check them with those which came from Activity and after that I need to find it in Groups entity and add it to Activity?
I must tell you that the scenario I wrote above is far from logical and easy solution that's why I'm concerned about it. Any ideas on how to set this relation between new object and existing ones?
Detailed explanation
When user opens app it has an empty Core Data. So to fill it he has to select some groups and based on this selection application is able to send a request for timetable which consists of Activities. So, if groups are selected, user switches to the timetable view and timetable with activities is downloaded from API. Each activity has also groups in it but I want to use groups that I've already created rather than adding new ones to Core Data.
Take a look at some code examples:
First of all I make a request to API to get all groups and in response I get JSON:
[
{
"id": 507,
"name": "KrDZIs3011Io",
"category": 1,
"category_name": "grupa dziekańska",
"regular": true
},
"..."
]
So I handle this like:
for (id group in responseObject) {
Group *groupEntity = [NSEntityDescription insertNewObjectForEntityForName:#"Group" inManagedObjectContext:tempContext];
groupEntity.name = [group valueForKey:#"name"];
groupEntity.cashID = [group valueForKey:#"id"];
groupEntity.caseInsensitiveName = [[group valueForKey:#"name"] lowercaseString];
groupEntity.selected = #NO;
}
I'll skip the part where I'm checking for duplicates and saving MOC.
After this app is able to fetch groups which user selects (groupEntity.selected = #YES) and based on that create a request for timetable. In response user get something like:
{
"_id":"g552g3328",
"params":{
"group_id":[
552,
3328
]
},
"version":"5096146ca522d316c87b217b83a6c4d2",
"activities":[
{
"id":18282,
"places":[
{
"id":97,
"name":"Paw. C s. A",
"full_name":"Pawilon C sala A",
"regular":true
}
],
"tutors":[
{
"id":266,
"name":"prof. UEK Paweł Lula",
"short_name":"P. Lula",
"moodle_url":"https://e-uczelnia.uek.krakow.pl/course/view.php?id=1034",
"regular":true
}
],
"groups":[
{
"id":552,
"name":"KrDZIs3011Io",
"type":1,
"type_name":"Grupa dziekańska"
},
{
"id":553,
"name":"KrDZIs3011Si",
"type":1,
"type_name":"Grupa dziekańska"
},
{
"id":554,
"name":"KrDZIs3012Si",
"type":1,
"type_name":"Grupa dziekańska"
}
],
"category":1,
"category_name":"wykład",
"name":"Teoria grafów",
"regular_course":true,
"notes":"",
"url":"",
"date":"2014-02-07",
"day_of_week":5,
"day_of_week_text":"Pt",
"starts_at":"9:35",
"ends_at":"14:45",
"regular_schedule":true,
"starts_at_timestamp":1391765400,
"ends_at_timestamp":1391771100,
"unit_ordinal_number":"1",
"unit_total_count":"15",
"canceled":false,
"canceled_reason":""
},
...
]
}
As you can see I have an array of activities and each activity has an array of groups (which already are in Database but not linked).
So here I create new Entity for timetable and new entities for Activities and when I get to the Groups array in Activity how should I link it to the groups I already have in database?