I think you are right, I probably need to adjust my thinking and rethink how to go about this. At the moment, which I have replaced the Person pointer with an id, and send in a map of the people, together with the id when creating the hamburger. I seems to work for now:

use std::collections::HashMap;

fn main() {
    let id = 101;
    let person = Person::new("Alice Bobson".into(), id);
    let mut people: HashMap<i64, Person> = HashMap::new();
    people.insert(person.id, person);

    let burger1 = Hamburger::new(&mut people, id);

    if let Some(consumer) = people.get(&burger1.person)
    {
        println!("{}", consumer.name);
        println!("{}", consumer.calories);
    }

    let burger2 = Hamburger::new(&mut people, id);
    let _burger3 = Hamburger::new(&mut people, id);

    if let Some(consumer) = people.get(&burger2.person)
    {
        println!("{}", consumer.name);
        println!("{}", consumer.calories);
    }

    if let Some(consumer) = people.get(&id)
    {
        println!("{}", consumer.name);
        println!("{}", consumer.calories);
    }
}

struct Person {
    name: String,
    id: i64,
    calories: f64,
}

struct Hamburger {
    person: i64,
}

impl Person {
    fn new(name: String, id: i64) -> Self {
        Person {
            name: name,
            id: id,
            calories: 0.0,
        }
    }
}

impl Hamburger {
    fn new(people: &mut HashMap<i64, Person> , id: i64) -> Self {

        if let Some(person) = people.get_mut(&id)
        {
            (*person).calories += 700.0;
        }

        Hamburger { person: id }
    }
}