There would be little point in him starting his own proceedings due to the legal costs involved, which in relation to divorce (without any legal advice and assistance with regard to finances) can top £1.5k with Court fees. Three weeks is not a long time in the world of divorce and it will take at least that for a solicitor to see your partner, take instructions, draft a petition etc etc. A solicitor would need to get a further copy of the marriage certificate from the Central Register which will take at least another 3 weeks. Just be a bit patient and maybe your partner can speak to his wife and ask her what the delay is