The official answer is; you don’t need to do that, just retain a read only copy of your old records for past periods. For future periods only transfer the starting balances from the end of the last period. See
Starting Balances: Enter starting balances | Fix starting balances
The more complete answer is, not as an automated process. It can be done but requires some computer skills. How much is actually done depends on the value a business places on having historical data in their new accounting system. How hard it is to do depends on what data is available on the old system and what you actually need to transfer across.You will need some computing / data manipulation skills or willing to finance someone with the skills to do this.
If you want to pursue importing data from you old computer system, then start by entering some data of each type manually into Manager. Both to see how time consuming it would be just to finish it this way and to help understand any automated method.
Next read the guide Use Batch Create and Batch Update functions. You will need to look at your already entered data with batch update to understand the required format.
Then import data without dependencies first, just as when you enter the data manually, it has to be done in the same order. This post is a little old by should give you an idea of what is involved How to batch import in manager - #11 by Patch