Earlier answers already describe the process of using triangulation to pinpoint the location of a specific phone better than I could describe it. However there is very little said about whether the investigators can figure out which exact phone the mail was sent from.
In traditional mail services where the user run an email client on their device and use SMTP to send the email to the server, the server will usually include the IP address of the client in the mail headers.
In cloud services where the user access email through a web browser or a vendor specific email app and use HTTP or HTTPS to send the email to the server, the server will usually not include the IP address of the client in the mail headers.
In the later case it is very likely that with a warrant the investigator could get the IP address through the cloud service provider.
But there is another question as to whether the IP address obtained in one of the two ways mentioned above will pinpoint the exact phone.
If your story is set somewhere between 2010 and 2020 it is quite likely that the internet provider is using carrier grade NAT due to shortage of IP addresses. And this can get in the way of figuring out which phone was connected to the server.
The eventual shortage of IP addresses was recognized by network engineers in the early 90s. By 1998 a solution was ready in the new IPv6 standard intended to replace the old IPv4 standard. But rather than working on the upgrade most internet providers have chosen to deploy carrier grade NAT instead, which will allow them to share a single IPv4 address between hundreds or thousands of users, though from the users perspective this will be a bit less reliable.
In case the internet provider the phone is connected to is already upgraded to the new IPv6 protocol, but the mail service only supports IPv4, the internet provider most likely uses NAT64. That is a kind of carrier grade NAT which happens to also translate packets between IPv4 and IPv6.
In terms of your storyline, NAT64 would be no different from carrier grade NAT. Though there could be some interesting arguments between investigator, mail provider, and internet provider as to who is responsible for the inability to find out which exact phone the email originated from. The internet provider could make a sound technical argument that the responsibility lies with the mail provider for not upgrading to IPv6. The mail provider would argue that they plan to do that a few months after everybody else have done it.
If you are going to have specific IP addresses show up in your script, there are three ranges of IPv4 addresses and one range of IPv6 addresses, you can use without worrying about the addresses belonging to somebody in particular.
192.0.2.0
-192.0.2.255
198.51.100.0
-198.51.100.255
203.0.113.0
-203.0.113.255
2001:db8::
-2001:db8:ffff:ffff:ffff:ffff:ffff:ffff