If both Wills are valid and haven’t been revoked you need to look at what the UK Will actually states regarding which assets it relates to and the payment of tax, your answer is simply there. If it’s the case looking at the Will that each countries succession laws are to be relied on (i.e the UK movable assets are under the Hong Kong Will), it will work as follows:
Hong Kong takes the same view as us on movable and immovable property i.e movable property is governed by the law the deceased was domiciled at the date of death, therefore there is no conflict in Private International Law with our two countries. It is therefore an asset controlled by the Hong Kong Will. There is no death tax in Hong Kong.
Foreign Personal representatives cannot be made liable in England and Wales for acts done under the foreign grant. They will only be liable if they intermeddle as an executor de son tort or apply for a UK resealed grant. In your case like Peter Double says, the Hong Kong Grant will need to be resealed (If moveable assets fall under Hong Kong law) in order to get the movable assets from the UK as it is the Hong Kong Will that deals with theses assets, not the UK Will. At this time all UK assets will need to be added to the IHT400 (IHT400 as its over £150,000) and the tax will be split between property that tax should be paid immediately on and tax that can be paid by instalments. The tax bill can therefore be split at that time. It means that you will need to work with the Hong Kong executors. Unless the Will says anything different.
As the tax that the Hong Kong executors must pay is paid before the grant, then this should prevent any problems on your end. You do not need to worry about the movable assets as it is not your problem, however it is important that you liaise with the Hong Kong executors as you do not want the IHT400 completed without the immovable asset placed on it. The obvious issue here is that you are reliant on the Hong Kong Executors being able to administer the estate quickly. From experience it takes a very long time to get a grant in Hong Kong.
If Hong Kong succession rules apply, perhaps you can get an agreement with the Hong Kong executors for permission for you to pay the movable assets directly from the bank accounts. You will then have a valid tax receipt for them when they apply?
With the above said, in most cases the UK Will will apply to all the UK assets and the executors will be given permission to pay the tax and you can simply deal with the estate as normal.