You can use REST API call Process API -> Current State to get the details about each step in the process and active tokens, you dont need the bpd id of source artifact to move the token just the token number which will be in the current state as well as the Process Inspector e.g. 2. Just search by name if the IME and it will be there with its BPD id.
But if you need to move a token from somewhere else to the IME you can get the bpdid from "Current State"
Then you can use the "move token" to move token to target step, you will need the instance id, token id e.g. 1,2,3 and target bpd id e.g. "bpdid:eb801ecb13cda6b9:51d8648a:15545cf9982:-7ff2"