Where do I find emails sent from the Samsung Mail App using a POP3 Mail Account? I have a Samsung Smartphone with a POP3 Mail Account on Samsung Standard Mail App.
I need the Emails I've sent with this account in my new Exchange Account on another device?
I think I may be able to transfer them if I find where they are stored on my phone.

Any ideas?
Maybe you can just move messages from POP3 Profile to IMAP Profile from your favorite email app.
If not, emails are stored in /data/data/com.android.email/databases/EmailProviderBody.db .
The non-rooting method

You can get these files with adb when usb-debugging is enabled in developer settings, then run from cmd.exe:
adb backup com.android.email


Convert backup.ab with android-backup-extractor after java is installed:
java.exe -jar abe.jar unpack backup.ab backup.tar


Extract EmailProviderBody.db from backup.tar with 7-zip.

Convert emails to *.eml with AndroidEmailExtractor after Groovy is installed.

Import the *.eml files in outlook express, move the messages to imap Sent folder, sync imap with new device.


The root method:
(If POP3 on your new device is ok for you)

View the ownership and file permissions from adb shell (new device)
adb shell
su
ls -lnZ /data/data/com.android.email/databases




Copy all EmailProvider.db* EmailProviderBody.db* to the new device (or folder database) from cmd
exit
exit
adb push C:\Android\Backup\email\databases /data/data/com.android.email/




Restore ownership and file permissions from adb shell, where 100xx is the uid from above
adb shell
su
chown -hR 100xx.100xx /data/data/com.android.email/databases
chmod 0660 /data/data/com.android.email/databases/*
chcon -hR u:object_r:app_data_file:s0 /data/data/com.android.email/databases


Reboot the device. Old emails should be restored to the new device.