Hi,
I’m sorry for your loss. Unfortunately you can’t put a finch in with budgies – they will end up killing it. As for being alone, it depends on how old he is. If this is a pair you have had for years and the other likely died of old age, then he might be best by himself. You could get him a mirror and some toys. He could live in a home with other birds, such as the budgies, but not in the same cage. This would give him some stimulation to hear their calls. If this is a young bird, just a 2-3 years old, then maybe you can find someone who wants a finch and would get him another companion.
Thank you for asking Lafeber,
Brenda