I wouldn't make him write at home - if it is something he finds hard, I would look to do other activities at home. What he needs to do is work on the muscles in his hands and fingers:
Playdough / plasticine / clay / (actual food) dough (for pizzas or making bread) - using rolling pins...... needing.... both good. Can also hide small items (paper clips / buttons / coins in playdough and get him to find them and pull them out
Pegs - putting clothes pegs on things and taking them off - can get them to literally hang washing out, or do games / races where they have to try to put 10 pegs on a piece of card or a piece of string before you / their sibling / friend
Wringing out wet tea towels / cloths / flannels etc - really good for finger strength
Peg boards - either the boards where you put the coloured pegs in to make patterns, or, even better, the ones where you stretch elastic bands round the little sticky up bits to make patterns - elastic bands are great for finger strength
Card games - putting the cards on a table or floor, face down and having to pick them up to turn them over is a good pincer grip practice - can be playing cards or lotto type games - anything where they are picking them up and turning them over. Teach him to play patience and you won't even have to sit and play with him
Games with tweazers - such as 'Operation' - where you have to use tweasers to move things. Can 'home make' similar with tweasers from your make up bag, or your granny's sugar tongs, and get them to move small things from one pot to another (smarties / raising / peas / pieces of pasta / etc)
Squeezing a sponge ball / water out of a washing up sponge / those rubbery, bouncy balls is also great for building strength.
Then, as mentioned above - writing is a struggle if their whole arm (gross motor) movement isn't as strong as it could be. For this you are looking for big, whole arm movements:
Fill an empty washing up liquid bottle with water and let them "draw" circles or letters or long lines on the patio or in the garden
Fill a bucket with water and give them a (decorators) paint brush and get them to "paint" the length of your fence or the back wall of your house with water
Pin some lining paper or even old newspaper sheets on the fence or wall and let them paint really big pictures, using as big an arm movement as they can
Go to the park and play on the monkey bars as often as you can
Also play on climbing frames
Pour water out of fairly full jugs, into smaller containers - pouring their own drinks when you are outside, or (less mess!) give them a big jug and smaller containers to play in the paddling pool or bath - it is really helpful to be able to pour from a realtively weighty jug accurately into smaller cups
Carry something like a chair - again, a weight at arms length
Encourage any way you can some 'commando crawling' (make you own garden obstacle course maybe, where he has to crawl under a sheet or some tarpaulin ??)
None of these will seem like "more work" to him, but all will help those muscles grow and be better and 'more trained' when he needs to use them for writing.