I bought a new phone (old: Samsung Galaxy J7; new: Huawei P30 Lite (old version)). On the old one, I had a lot of WhatsApp chats. When I then installed WhatsApp on the new cell phone and entered my number, which is also specified on WhatsApp on the old cell phone, WhatsApp was on the new cell phone, but the chats on the old one. After I switched on the WLAN from the old cell phone, I came to the "beginning", to the point where I should enter my number.
If I entered my number on the old cell phone now, would I get my OLD chats again or would I just transfer the chats on my new cell phone to it?
I can't say whether the chats still exist; in any case, they won't just get on the new cell phone like this. You should have done a back-up before, maybe it's too late for that now.
Did you create a backup in your Google Driver?
Alternatively, you can copy the chats manually.
Unfortunately I didn't make a backup.
Is there no alternative?
No? You could at most enter the phone number again in the old cell phone. If the chats still exist, you can do a backup of the chats in the settings and load them on the new phone.
Register your mobile number again with WhatsApp on your old mobile phone, there the chats are normally saved, as long as you haven't reset it, then you can make a WhatsApp chat backup. You can then register your phone number with the new one and, depending on how you made the backup, import it again:-) However, the current WhatsApp messages that you have already written on the new phone can be lost.
