If a Flash-SIP call is established, can SIP user initiate a conference call and invite another SIP user?

Flash phone is able to participate in a conference which is established via a confbridge(PBX).

For example:
1. Flash phone calls to a conf bridge number 001.
2. SIP phone calls to a confbridge 001.
3. They are in the conference room.

In the case when Flash phone – SIP phone call is established, you can not add a third phone to the established call.
Sure if the Flash-SIP call was established via a conference number, you can do it.

Another solution in this situation is to transfer the Flash phone call to the conference call number.
1. SIP phone transfers this call to a conference number.
2. SIP phone dials the conference number itself.
3. Third phone is calling to the conference number.