A transfer from an existing ISA (including a Help to Buy ISA) into a Cash or Stocks & Shares ISA does not count again towards your £20,000 annual ISA allowance, which means if your ISA balance exceeds £20,000, you can transfer the full amount.
A transfer from an ISA into a Lifetime ISA does count towards the £4,000 LISA annual allowance, as you’ll earn the 25% government bonus on your transferred funds. This means that you can only transfer up to £4,000 per tax year from an ISA into a LISA - if your current ISA balance exceeds £4,000, you’ll need to split the transfer over multiple tax years. For example, if you transferred £4,000 from an ISA held with another provider into a Moneybox ISA, and the money was originally paid into the ISA in a previous tax year, the transfer would not count again towards your current tax year’s £20,000 allowance.
However, if you transferred £4,000 from an ISA into a Lifetime ISA, the transfer would still use up your Lifetime ISA’s £4,000 allowance for the current tax year. If the money was originally paid into the ISA in a previous tax year, only your £4,000 LISA allowance would be affected - your £20,000 annual ISA allowance would not be used by the transfer into the LISA.