There are several problems here.
First, Your if statement probably doesn't do what you think it does.
You've written:
            if lastname and firstname and phone in firstfile: 
That statement is more accurately written like this:
            if (lastname) and (firstname) and (phone in firstfile): 
That is, you are treating lastname and firstname as boolean
values, which means they will always evaluate to True when
non-empty, and then you're checking if phone in firstfile.
This is your second problem: you can't use in to check if a string
exists in a file; that condition will always return False. You need to read the file content into a variable, giving you something like:
    with open('Phonebook','r') as firstfile, open('Reception','a') as secondfile:
        
            # read the file into a string
            firstcontent = firstfile.read()
            # now we can check if `<some_string_var> in firstcontent`
            if lastname in firstcontent and firstname in firstcontent and phone in firstcontent: 
                
                secondfile.write(imp)
                print('phonebook exported!')
            else:
                print('This phonebook doesn\'t exist !')
You could simplify that condition using the all builtin:
if all(x in firstcontent for x in [firstname, lastname, phone]):
Here's a demonstration of it working. Assuming that I have a file "Phonebook" that contains the following content:
bob example 123-456-7890
And this code:
firstname = input("Enter a firstname:")
lastname = input("Enter a lastname:")
phone = input("Enter a phone number:")
imp = f"'{firstname}''{lastname}''{phone}'"
with open("Phonebook", "r") as firstfile, open("Reception", "a") as secondfile:
    # read the file into a string
    firstcontent = firstfile.read()
    # now we can check if `<some_string_var> in firstcontent`
    if all(x in firstcontent for x in [firstname, lastname, phone]):
        secondfile.write(imp)
        print("phonebook exported!")
    else:
        print("This phonebook doesn't exist !")
If I provide responses that match an entry in the phonebook:
$ python phonebook.py
Enter a firstname:bob
Enter a lastname:example
Enter a phone number:123-456-7890
phonebook exported!
$ cat Reception
'alice''example''123''bob''example''123-456-7890'
Whereas if I provide a response that doesn't match:
$ python phonebook.py
Enter a firstname:alice
Enter a lastname:example
Enter a phone number:987-654-3210
This phonebook doesn't exist !