Please do not send personal messages with general questions like this. I have moved your post to the public forum.
I have no idea what TC4 is. In general, however, you cannot migrate data from one accounting system to another without custom software. The expense of that is seldom justifiable. Even different programs by the same developer are often not compatible. Manager’s approach to migration from other accounting systems is to set starting balances matching ending balances from your old system. See https://www.manager.io/guides/15718.
If you want to migrate customer or supplier information, inventory information, and so on, batch operations can be useful. But that is not for the faint of heart. See https://www.manager.io/guides/9572. You will likely get involved with a great deal of data manipulation in spreadsheets along the way. Forget about the idea of whatever you mean by “mapping” as a phase 2. You will either be able to massage your data into a form acceptable by Manager or not. You will not be able to enter it and map anything later.