SAYE/SIP into SIPP

Previn

Hi,

Gov UK website states in respect to SAYE schemes on maturity....
You might have to pay Capital Gains Tax if you sell the shares - but not if you put them into an Individual Savings Account (ISA) or pension as soon as you buy them.

I have used all my CGT allowance this year & also filled an ISA with £20k from matured SIP scheme.

I have more shares from a SIP($6k U.S.) & also will soon have more SAYE shares (£13k UK) matured.
In order to avoid CGT on the SAYE shares then I'm looking to transfer directly into my SIPP as per Gov rules above.
I'm not aware of anyone who's has done this & AJ Bell advised they would not support.
Has anyone else actually done this into a UK SIPP provider? I'm mostly focused on the SAYE transfer but SIP would be useful also.

Many Thanks