My situation is a bit different as I had to get my sons father to sign over sponsorship as he was living here and was moving to another country and my son was staying with me.

A friend of mine brought her son here in the same situation. I am not sure on the paperwork that was required but it obviously can be done. As you all have the same surname and there is no father listed on the birth certificate I am not sure what they will ask for. It may be a little messy and incomprehensable to local authorities but I can assume that once you start the RP proceedings for your family and all the names are the same it may go without a glitch.

Just a quick question, did you legally adopt your step-daughter?

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"Diplomacy is the art of saying 'Nice doggie' until you can find a rock - Will Rogers"