Appendix FM-SE says evidence of self-employment outside the UK should be a reasonable equivalent of the UK list. If the sponsor is returning to the UK to continue being self-employed, they also need evidence of the business's next steps here, starting within three months of their return.
A reasonable equivalent means the foreign documents that show the same facts: income declared, tax assessed, money received and the business still trading. A Spanish autónomo might have the Modelo 100 return, the Modelo 130 quarterly payments, the alta in the RETA social security register and statements from two accounts. A French micro-entrepreneur might have the avis d'imposition, URSSAF declarations and an extrait from the business register. The rules don't name foreign forms, so we won't pretend they do.
A sponsor coming back to the UK to carry on the same business needs one more piece of evidence from paragraph 8A: for example, an application for a licence to trade, the purchase or rental of business premises, a signed contract for work, or a partnership or franchise agreement. If those documents were drawn up abroad, they need translating too.