Whether the move is effective or wise in this case, is quite another question. It seems to me likely the Iranians will take it as confirmation that she is a spy. I would urge the Iranian government to take this course; they should now declare the the adoption of the case as a state dispute proves that Zaghari Ratcliffe is a spy, and having been proven right before the world, they will let her go as an example of mercy and compassion.
There are two fundamental points here. The first is that Iran has been subjected for years to crippling sanctions and an international campaign of hate spread by western government propaganda and their MSM. Western governments have aligned themselves with Saudi and Israeli sponsored brutal proxy wars against Shia communities across the Middle East, which look to Iran for protection. If the Iranian government is defensive and suspicious, is that really surprising? The week after the British government declared Hezbollah, the political and security organization of Lebanese Shias, to be nothing but a terrorist organisation, do the Tories really think the Iranians will be looking kindly on them and their demands over Zaghari Ratcliffe?
The second point is that the entire purpose of the state "adopting" a case, is to make available the dispute resolution mechanisms which operate between states. But the UK only a few days ago repudiated the International Court of Justice, the final arbiter of such disputes, over the Chagos Islands. As the UK shows total contempt for international law, this attempt to access its remedies will be met with derision by the wider international community.