Move to iOS - Can't transfer all my messages from Android to iPhone

Dear Apple Community,

I'm reaching your help here because I need your help with this issue. 

Simply said, I bought an iPhone and I just wanted to transfer all my data [including just messages (SMS), contacts, WhatsApp chats] from my Android device to the iPhone.

I used app called Move to iOS developed by Apple.

But the problem is, while transfering the data, everything works pretty fine, contacts is transfered, WhatsApp messages as well, until I check "transfered" messages (SMS). 

I simply can not see all the messages, it appears like I am texting with myself only. Until February (screens sent below). I can only see messages from February and older. And I'm not even sure if there is all messages, because I'd have to scroll for a long time to figure it out. 

I tried delete my iPhone for like 15 times and tried all possible methods, nothing works for me. Once happened that, I couldn't see my messages. Even from February and older. I just saw messages from sender. It appeared like two times like that. Then I deleted my iPhone again and then it's what it was before. I can see messages sent by me, and I'm sure there is a lot of missing messages yet - on screenshots there is a conversation (between 11/03 and 04/02) , which is not screened, because it's all the same (messages just by me, so I decided to not screenshot it since it's pretty unnecessary.) First message I can see from sender is from like a week ago (a picture) and then from February and older, as I said before. 

I'm pretty clueless already. I don't want to use iPhone without my messages, because those messages mean a lot to me, and I'm not talking about all the informations I got there, which I need for sure. 

I'd be very grateful if you could fix it somehow or at least help me to solve this unpleasant problem. 

I'm sending some screenshots to you, so you can see what it does - screenshots also include the problem what it does only like two times (Seeing messages only from sender), but now I'm seeing messages sent by me again, as I said before, hope it's clear to you - Simply I'm just going to show you all the problems I faced, so you can recognize this issue easier, hopefully.

Greetings,

Michal Hořínek, Czech Republic